9 — 11 SEP’24

Europeanctuarial Journal
onference

ISEG, Lisbon, Portugal

vited
peakers 6 European

9 — 11 SEP’24th

Actuarial Journal
Mercè Claramunt
Conference

Universitat de Barcelona

Loisel
ISEG, Lisbon,Stéphane
Portugal
Université Lyon 1

Marie Kratz

ESSEC Business School

portant Dates
Abstract
SubmissionInvited
Speakers→ 31 May 2024

Abstract
Acceptance→ 10 June 2024
Mercè Claramunt

Universitat de Barcelona

Early Bird
Registration Fee→ 28 June 2024
Marie Kratz

ESSEC Business School

Stéphane Loisel
Université Lyon 1

anizing Committee

Importanteszka Bergel | Alexandra
MouraDates| Alfredo Egídio dos Reis | Carlos Oliveirao Andrade e Silva | Manuel Guerra| Nuno M. Brites | OnofreSimões | Rui Cardoso
Abstract
Abstract
Early Bird
Submission→ 31 May 2024

Acceptance→ 10 June 2024

Registration Fee→ 28 June 2024

w more hereajc2024@gmail.com

Organizing Committee
Agnieszka Bergel | Alexandra Moura | Alfredo Egídio dos Reis | Carlos OliveiraJoão Andrade e Silva | Manuel Guerra | Nuno M. Brites | Onofre Simões | Rui Cardoso

Know more here

9 — 11 SEP’24

European Actuarial Journal Conference 2024
6th European
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024
Actuarial Journal
ISEG, Lisbon, Portugal
Conference

Organizing Committee:

InvitedSpeakers

Agnieszka Bergel
Alexandra Moura
Alfredo Egı́dio dos Reis
Carlos OliveiraJoão Andrade e Silva
ManuelGuerraMercè
Claramunt
Universitat
de Barcelona
Nuno
M. Brites
Onofre Simões
Rui Cardoso

Marie Kratz

ESSEC Business School

Stéphane Loisel
Université Lyon 1

Important Dates

Abstract
Submission→ 31 May 2024

Abstract
Acceptance→ 10 June 2024

Early Bird
Registration Fee→ 28 June 2024

Organizing Committee
Agnieszka Bergel | Alexandra Moura | Alfredo Egídio dos Reis | Carlos OliveiraJoão Andrade e Silva | Manuel Guerra | Nuno M. Brites | Onofre Simões | Rui Cardoso

Sponsors:
Know more here

eajc2024@gmail.com

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Contents
TIME TABLE

1

PROGRAM
4th
MONDAY, SEPTEMBER 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
TUESDAY, SEPTEMBER 10th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
WEDNESDAY, SEPTEMBER 11th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
ABSTRACTS
17
MONDAY, SEPTEMBER 9th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
PLENARY SESSION I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
PARALLEL SESSIONS I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
PARALLEL SESSIONS II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
PARALLEL SESSIONS III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
TUESDAY, SEPTEMBER 10th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
PLENARY SESSION II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
PARALLEL SESSIONS IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
PARALLEL SESSIONS V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
WEDNESDAY, SEPTEMBER 11th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
PLENARY SESSION III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
PARALLEL SESSIONS VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Author index

121

Speaker index

124European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

TIMETABLE
SUNDAY, SEPTEMBER 8th
17:00

Welcome Reception (rooftop)

MONDAY, SEPTEMBER 9th
8:30–9:30

Registration and get together

9:30–10:00

Opening Session (Aud. 1)

10:00–11:00

Plenary
SessionAuditorium 1

11:00–11:20

11:20–12:40

Coffee BreakParallelSessions

Auditorium 1

Climate Risks 1

Auditorium 2

Risk Management 1

Auditorium 3

Data Science 1

Anfitheatre 4Life Insurance 1

Room CTT

Risk Theory

12:40–14:30

14:30–15:50

Lunch

ParallelSessions

Auditorium 1

Mortality 1

Auditorium 2

Nonlife Insurance Mathematics 1

Auditorium 3

Risk Management 2

Anfitheatre 4

Ratemaking

15:50–16:10

16:10–17:30

Stéphane Loisel:
Climate Change, sustainability andprevention

Coffee BreakParallelSessions

Auditorium 1

Mortality 2

Auditorium 2

Statistical Methods 1

Auditorium 3

Mathematical Finance 1

Anfitheatre 4

Nonlife Insurance Mathematics 2

1

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

TUESDAY, SEPTEMBER 10th
9:00–9:30
9:30–10:30

Registration
Plenary
SessionAuditorium 1

10:30–10:50

10:50–12:10

Coffee BreakParallelSessions

Auditorium 1

Climate Risks 2

Auditorium 2

Mathematical Finance 2

Auditorium 3

Data Science 2

Anfitheatre 4Life Insurance 2

12:10–14:00

14:00–15:20

Merce Claramunt:
Reverse mortgages: impact on household
financial sustainability

Lunch

ParallelSessions

Auditorium 1

Life Insurance 3

Auditorium 2

Nonlife Insurance Mathematics 3

Auditorium 3

Health Insurance

Anfitheatre 4

Reinsurance

15:20–16:00

Coffee Break

18:00–19:30

Visit to Orient Museum

19:30–20:00

Welcome drinks (Orient Museum)

20:00–22:00

Gala dinner (Orient Museum)2

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

WEDNESDAY, SEPTEMBER 11th

9:30–10:30

Plenary
SessionAuditorium 1

10:30–10:50

10:50–12:10

Marie Kratz:
Confronting emerging risks with flexible
general models; a focus on cyber risk
Coffee BreakParallelSessions

Auditorium 1

Climate Risks 3

Auditorium 2

Mathematical Finance 3

Auditorium 3

Statistical Methods 2

Anfitheatre 4

Pensions

12:10–12:40

Closing Session (Aud.1)

12:40–14:30

Lunch

3

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

PROGRAMMONDAY, SEPTEMBER 9th
8:30–9:30 Registration and get together
9:30–10:00 Opening Session
10:00–11:00 PLENARY SESSION I: Stéphane Loisel
CLIMATE CHANGE, SUSTAINABILITY AND PREVENTION

Aud.1(p.17)

11:00–11:20 Coffe Break
11:20–12:40 PARALLEL SESSIONS I
Climate Risks 1 (Chair: José Garrido)

Aud.1

Séverine Arnold
AN INTERGENERATIONAL RICE MODEL APPROACH TO ASSESS THE IMPACT OF
CLIMATE CHANGE ON SOCIAL SECURITY SYSTEMS UNDER SHAREDSOCIOECONOMIC PATHWAYS(p.17)
Nick Jessop
ASSESSING CLIMATE CHANCE SCENARIOS FOR VARIOUS COHORTS OFPENSIONERS: INSIGHTS FOR NEST PENSIONS(p.19)Nan Zhou
STATISTICAL METHODOLOGIES TO ASSESS THE IMPACT OF CLIMATE CHANGE ON
INSURANCE SUSTAINABILITY. THE CASE OF HAILSTORM RISK IN SPANISHAGRICULTURAL INSURANCE-WINEGRAPES(p.19)
José Garrido
THE FRENCH ACTUARIAL CLIMATE INDEX AND ITS APPLICATION TO
PARAMETRIC INSURANCE

4(p.21)

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Risk Management 1 (Chair: Stefan Weber)

Aud.2

Pietro Millossovich
STRESS TESTING WITH f -DIVERGENCES(p.22)

Xenxo Vidal-Llana
QUANTILE REGRESSION AND PORTFOLIO REFINEMENT: ADDRESSING EXTREMEBEHAVIORS IN RISK MANAGMENT(p.23)
Yukio Muromachi
A TERM STRUCTURE MODEL OF DEFAULT-FREE AND DEFAULTABLE
INTEREST RATES WITH REGIME-SWITCHING PROPERTIES: APPLICATION TO
FORWARD-LOOKING STATISTICAL RISK MANAGEMENT(p.24)
Stefan Weber
INTERNAL MODELS: BACKTESTING AND SIMULATING DISTORTION RISKMEASURES(p.25)

Data Science 1 (Chair: Arthur Charpentier)

Aud.3

Stefano Demartis
THE CALCULATION OF SCR UNDER SOLVENCY II: A VINE COPULA-GARCHAPPROACH(p.27)Oguz Koc
INSURANCE FRAUD DETECTION VIA CLUSTERING-BASED FUZZYCLASSIFICATION ON NOISY UNBALANCED DATASETS(p.28)

Matteo Malavasi
CYBER RISK TAXONOMIES: STATISTICAL ANALYSIS OF OPERATIONALCYBERSECURITY RISK CLASSIFICATIONS(p.29)

Arthur Charpentier
CALIBRATION OF INSURANCE MODELS(p.30)

5

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Life Insurance 1 (Chair: Apostolos Bozikas)

AF4

Theis Bathke
ESTIMATION OF BIVARIATE TRANSITION RATES IN LIFE INSURANCE(p.31)

Julie Bjørner Søe
A STATE-DEPENDENT APPROACH TO OPTIMAL CONSUMPTION, INVESTMENT,AND LIFE INSURANCE BY RISK-ADJUSTED UTILITIES(p.32)
Laura González-Vila
REDUCING THE GENDER GAP IN OLDER ADULT FINANCES THROUGH REVERSE
MORTGAGES(p.34)
Apostolos Bozikas
SUBJECTIVE SURVIVAL PROBABILITIES IN LIFE INSURANCE

Risk Theory (Chair: Konstadinos Politis)(p.36)
Room CTT

Renata G. Alcoforado
ON A PENALTY FUNCTION IN THE ERLANG RENEWAL DUAL RISK MODEL UNDERINDEPENDENT RANDOMISED OBSERVATIONS(p.37)
Lazaros Kanellopoulos
SOME APPROXIMATIONS RESULTS FOR RUIN PROBABILITIES IN THE CLASSICALRISK MODEL(p.38)
Harold A. Moreno-Franco
OPTIMAL RISK POLICIES AND PERIODIC DIVIDEND STRATEGIES FOR AN
INSURANCE COMPANY(p.39)

Konstadinos Politis
SOME NEW APPROXIMATIONS FOR THE DENSITY OF RUIN TIME

(p.39)

12:40–14:30 Lunch

Rooftop6

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

14:30–15:50 PARALLEL SESSIONS II
Mortality 1 (Chair: Xavier Milhaud)

Aud.1

Şule Şahin
MORTALITY MODELS: PRE- AND POST-COVID INSIGHTS(p.40)

Luca De Mori
MORTALITY FORECASTING VIA MULTI-TASK NEURAL NETWORKS(p.42)

Xavier Milhaud
IMPACT OF HEAT WAVES ON MORTALITY: EXTENSION OF LONGEVITY MODELSTO ACCOUNT FOR GLOBAL WARMING(p.43)

Nonlife Insurance Mathematics 1 (Chair: Mustafa Asım Özalp)

Aud.2

Hassan Abdelrahman
HMM-BASED COX MODELS FOR IBNR RESERVING(p.43)

Marcin Szatkowski
ONE-YEAR AND ULTIMATE CORRELATIONS IN DEPENDENT CLAIMS RUN-OFF
TRIANGLES(p.44)
Mustafa Asım Özalp
ADVANCING ACTUARIAL CLAIM MODELING: ADDRESSING UNOBSERVED RISKFACTORS WITH A HMM(p.45)

Risk Management 2 (Chair: Yevhen Havrylenko)

Aud.3

Andrei Craciunescu
A PUBLIC DIRECTORS AND OFFICERS LIABILITY RISK QUANTIFICATION MODELBASED ON GENERALIZED LINEAR MODELS(p.47)
Ajla Nurkanović
OPTIMAL INVESTMENT AND SUSTAINABLE TAXATION(p.48)

Kristien Doumen
INSURANCE PRODUCT DESIGN AND ATTRIBUTES RELATING TO SOCIAL AND
ENVIRONMENTAL SUSTAINABILITY: A SYSTEMATIC REVIEW ON RETAIL MOTOR
INSURANCE(p.49)
Yevhen Havrylenko
ASSET-LIABILITY MANAGEMENT WITH LIQUID AND FIXED-TERM ASSETS

7(p.51)

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Ratemaking (Chair: Pierre-Olivier Goffard)

AF4

Juan Sebastián Yánez
WEEKLY DYNAMIC MOTOR INSURANCE RATEMAKING WITH A TELEMATIC
SIGNALS BONUS-MALUS SCORE(p.52)
Julien Trufin
CONVEX AND LORENZ ORDERS UNDER BALANCE CORRECTION IN NONLIFE
INSURANCE PRICING(p.54)
Pierre-Olivier Goffard
MARKET-BASED INSURANCE RATEMAKING(p.54)

15:50–16:10 Coffee Break
16:10–17:30 PARALLEL SESSIONS III
Mortality 2 (Chair: Peter Hatzopoulos)

Aud.1

M. Marino
NON-CHRONOLOGICAL AGES AND THE LIFETIME SHIFTING: INVESTIGATING A
NEW PARADIGM IN MORTALITY MODELING AND FORECASTING(p.55)
Funda Karaman
A MODIFIED POISSON INVERSE GAUSSIAN LEE-CARTER MORTALITY MODEL (p.56)
George Streftaris
BAYESIAN MODELLING FOR CANCER MORTALITY – INEQUALITIES, COVID-19
IMPACT AND FUTURE PROJECTIONS(p.57)
Peter Hatzopoulos
A NOVEL FRAMEWORK OF STOCHASTIC MORTALITY MODELLING

8(p.58)

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Statistical Methods 1 (Chair: Christian Furrer)

Aud.2

Christoffer ØhlenschlægerHETEROGENEOUS EXTREMES IN THE PRESENCE OF RANDOM COVARIATES ANDCENSORING(p.59)
Selim Gatti
MODELING LOWER-TRUNCATED AND RIGHT-CENSORED INSURANCE CLAIMSWITH AN EXTENSION OF THE MBBEFD CLASS(p.60)
Łukasz Delong
ISOTONIC REGRESSION FOR VARIANCE ESTIMATION AND ITS ROLE IN MEAN
ESTIMATION AND MODEL VALIDATION(p.62)
Christian Furrer
AALEN–JOHANSEN: REFRESHED AND REFINED(p.62)

Mathematical Finance 1 (Chair: Debora Daniela Escobar)

Aud.3

Atibhav Chaudhry
CONVEX HEDGERS AND FAIR CONVEX COST-OF-CAPITAL VALUATIONS IN A
SINGLE PERIOD FRAMEWORK(p.63)
Edouard Motte
EFFICIENT HEDGING OF LIFE INSURANCE PORTFOLIO FOR LOSS-AVERSE
INSURERS(p.64)

Oussama Belhouari
THE THREE-STEP METHOD IN A DYNAMIC SETTING(p.65)

Debora Daniela Escobar
OPTIMAL REINSURANCE MAXIMISING DIVIDENDS: AN INFINITE-DIMENSIONALAPPROACH AND NUMERICAL RESULTS(p.65)

9

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Nonlife Insurance Mathematics 2 (Chair: Jorge Yslas)

AF4

Fabio Colpo
OPTIMAL DIVIDEND FOR AN ORNSTEIN UHLENBECK SURPLUS(p.67)

Elisabete Fino
ON THE MINIMIZATION OF THE RUIN PROBABILITIES OF TWO INSURERS IN A
RISK-SHARING SCENARIO(p.67)
Constantin Siggelkow
ENHANCING SME FACTORING: A STACKELBERG GAME-BASED HYBRID PRICING
MODEL(p.68)
Jorge Yslas
CURE MODELS: FROM MIXTURE TO MATRIX DISTRIBUTIONS(p.69)TUESDAY, SEPTEMBER 10th
9:00–9:30 Registration
9:30–10:30 PLENARY SESSION II: Merce Claramunt

Aud.1
REVERSE MORTGAGES: IMPACT ON HOUSEHOLD FINANCIAL SUSTAINABILITY(p.70)

10:30–10:50 Coffee Break
10:50–12:10 PARALLEL SESSIONS IV
Climate Risks 2 (Chair: Nan Zhou)

Aud.1

Ivan Fonseca Diaz
INTERGENERATIONAL-DICE MODEL: AN INTEGRATED ASSESSMENT ANALYSISON THE EFFECTS OF CLIMATE CHANGE ON SOCIAL SECURITY SYSTEMS(p.71)
Nora Muler
OPTIMAL DIVIDEND STRATEGIES FOR A CATASTROPHE INSURER WITHIRREVERSIBLE CLIMATE CHANGE(p.72)Nan Zhou
ON THE DEFINITION OF AN ACTUARIAL CLIMATE INDEX FOR THE IBERIANPENINSULA(p.73)

10

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Mathematical Finance 2 (Chair: Griselda Deelstra)

Aud.2

Betty Guo
OPTION PRICING WITH GIVEN CONSTRAINTS AND ITS APPLICATION TO LIFE
INSURANCE CONTRACTS(p.75)
Laurena Ramadani
GANs FOR PORTFOLIO OPTIMIZATION(p.76)

D.-J. Economides
PERPETUAL AMERICAN OPTIONS IN A JUMP DIFFUSION MODEL WITH TWO-SIDEDJUMPS UNDER POISSON OBSERVATIONS(p.78)
Griselda Deelstra
ACCELERATED COMPUTATIONS OF SENSITIVITIES FOR XVA(p.78)

Data Science 2 (Chair: Peter Hieber)

Aud.3

Luis Cespedes
LEVERAGING RELATIONAL DATABASES FOR SPATIAL ANALYSIS AND DECISION
MAKING IN INSURANCE(p.79)
James Hannon
GEO-SPATIAL MODELLING OF VEHICLE CRIME IN NORTHERN IRELAND USINGCOMPUTER VISION TO IDENTIFY ENVIRONMENTAL FACTORS(p.81)
Helton Graziadei
CHALLENGES IN ACTUARIAL LEARNING FOR LOSS MODELING OF BRAZILIANSOYBEAN CROPS(p.82)
Peter Hieber
EFFICIENTLY COMPUTING ANNUITY CONVERSION FACTORS VIA FEED-FORWARD
NEURAL NETWORKS(p.84)

11

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Life Insurance 2 (Chair: Andrey Ugarte Montero)

AF4

Chia-Chih Chao
A ROBUST FRAMEWORK FOR MITIGATING BIAS AND VARIANCE IN MORTALITY
PREDICTION IN LIFE INSURANCE(p.85)
D. Rodrigues
RISK ADJUSTMENT MODELING FOR LONGEVITY RISK

(p.86)

Annamaria OlivieriBASIC PERFORMANCE METRICS FOR LONGEVITY-LINKED ANNUITANTS(p.87)

Andrey Ugarte Montero
IMPROVING SURVIVAL RATE ESTIMATES USING INSURED AMOUNTS(p.87)

12:10–14:00 Lunch

Rooftop

14:00–15:20 PARALLEL SESSIONS V
Life Insurance 3 (Chair: Mark Van Lokeren)

Aud.1

Alexandra Dias
RISK MANAGEMENT IN THE RETIREMENT DECUMULATION PHASE(p.88)

Massimo Costabile
VALUING LIFE INSURANCE POLICIES WITH STOCHASTICALLY CORRELATEDINTEREST RATES AND MORTALITY(p.89)
Barbara RogoPERFORMANCE PROFILES OF PROFIT SHARING INSURANCE CONTRACTS WITH
RETURN TARGET FINANCIAL STRATEGY UNDER IFRS 17(p.89)Mark Van Lokeren
GENERAL BOUNDS FOR FUNCTIONALS OF THE LIFETIME, COMPATIBLE WITH LIFETABLES(p.91)

12

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Nonlife Insurance Mathematics 3 (Chair: Jaap Spreeuw)

Aud.2

Alaric J.A. Müller
PLUVIAL FLOOD RISK MODELLING USING FLOOD RISK MAPS AND AN ADVANCEDSTOCHASTIC WEATHER GENERATOR: THE CASE OF AUSTRIA(p.92)
Georgios Pitselis
CREDIBILITY DISTRIBUTION ESTIMATION IN A HIERARCHICAL FORM

(p.93)

George Tzougas
MULTIVARIATE CLAIM COUNT REGRESSION MODEL WITH VARYINGDISPERSION AND DEPENDENCE PARAMETERS(p.94)

Jaap Spreeuw
GED SPLINE ESTIMATION OF MULTIVARIATE ARCHIMEDEAN COPULAS BASED ON
THE WILLIAMSON D-TRANSFORM(p.94)

Health Insurance (Chair: Ian Duncan)

Aud.3

Laura Iveth Aburto Barrera
DEVELOPMENT OF MULTIMORBIDITY PATTERNS IN OLDER ADULTS IN
SWITZERLAND: A COMPETING RISKS MODELING APPROACH(p.95)

Renata G. Alcoforado
SOCIOECONOMIC BENEFITS OF THE BRAZILIAN INSS ATESTMED PROGRAMME(p.97)
Ayşe Arık
REFINING CANCER INSURANCE PRICING: INSIGHTS FROM SEMI-MARKOV
MODELLING(p.98)

Ian Duncan
A POISSON-TWEEDIE COLLECTIVE RESERVING MODEL FOR ESTIMATINGPROVIDER GAIN-SHARING PAYMENTS(p.99)

13

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Reinsurance (Chair: Ozenc Murat Mert)
Aleksandar Arandjelović
REINSURANCE WITH NEURAL NETWORKS

AF4(p.100)Julia Eisenberg
REINSURANCE PRICE AS A TWO-STATE MARKOV JUMP PROCESS: HOW TO FIND
THE OPTIMAL STRATEGY(p.101)Phuong Nguyen
OPTIMAL REINSURANCE TO MINIMIZE THE PROBABILITY OF PARISIAN RUIN
WITH EXPONENTIAL GRACE PERIOD(p.101)
Ozenc Murat Mert
OPTIMAL RISK DIVERSIFICATION FOR A REINSURANCE COMPANY UNDER A
STOCHASTIC CLAIM APPROACH(p.102)

15:20–16:00 Coffee Break
18:00–19:30 Visit to Orient Museum
19:30–20:00 Welcome drinks

Orient Museum

20:00–22:00 Gala Dinner

Orient Museum

WEDNESDAY, SEPTEMBER 11th
9:30–10:30 PLENARY SESSION III: Marie Kratz

Aud.1

CONFRONTING EMERGING RISKS WITH FLEXIBLE GENERAL MODELS;
A FOCUS ON CYBER RISK
(p.104)10:30–10:50 Coffee Break14

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

10:50–12:10 PARALLEL SESSIONS VI
Climate Risks 3 (Chair: Despoina Makariou)

Aud.1

Roberto Carcache Flores
MITIGATING FLOOD RISK WITH CAT BONDS: A NEW ORLEANS CASE STUDY (p.105)
Marina Solomou
DESERT DUST STORM INSURABILITY: A PRIMER(p.105)Samira Aka
DISCRETE MULTIVARIATE GENERALIZED PARETO DISTRIBUTION WITH
APPLICATION TO THE STUDY OF DROUGHTS(p.107)

Despoina Makariou
A CAUSAL MACHINE LEARNING APPROACH FOR ESTIMATING HETEROGENEOUS
TREATMENT EFFECTS IN THE PRIMARY CATASTROPHE BOND MARKET(p.108)Mathematical Finance 3 (Chair: Antonino Zanette)

Aud.2

Jean René Mwizere
A SUSTAINABLE APPROACH TO RETIREMENT INVESTING FOR THE LONG HAUL
(p.109)Felix Sachse
TERM STRUCTURE SHAPES IN THE SVENSSON FAMILY(p.110)Thorsten Schmidt
AFFINE VALUATION OF VARIABLE ANNUITIES(p.111)

Antonino Zanette
ENHANCING VALUATION OF VARIABLE ANNUITIES IN LÉVY MODELS WITH
STOCHASTIC INTEREST RATES(p.113)

Statistical Methods 2 (Chair: Alfred Müller)

Aud.3

Udo Kamps
PREDICTION INTERVALS FOR PARETO RECORD CLAIMS – COMPARISONS ANDAPPLICATIONS(p.114)
Alessandro Barbiero
APPROXIMATION OF ABSOLUTELY CONTINUOUS RANDOM VARIABLES FOR THE
ASSESSMENT OF THE DISTRIBUTION OF COMPOUND SUMS
(p.115)
Alfred Müller
STOCHASTIC ORDERS UNDER UNCERTAINTY

15(p.116)

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Pensions (Chair: M. Carmen Boado-Penas)

AF4

Philipp C. Hornung
INVESTIGATING TRADE-OFFS IN THE DESIGN OF SMOOTH PENSION PRODUCTS(p.117)
Sascha Günther
TONTINES WITH MONEY-BACK GUARANTEE(p.117)

Sarah Kaakai
TIME-CONSISTENT PENSION POLICY WITH MINIMUM GUARANTEE AND
SUSTAINABILITY CONSTRAINT(p.118)

M. Carmen Boado-Penas
THE SURVIVOR DIVIDEND TO ENHANCE PENSION ADEQUACY IN NOTIONAL
DEFINED CONTRIBUTION SCHEMES(p.120)

12:10–12:40 Closing Session

Aud.1

12:40–14:30 Lunch

Rooftop16

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

ABSTRACTS
MONDAY, SEPTEMBER 9th
PLENARY SESSION I
CLIMATE CHANGE, SUSTAINABILITY AND PREVENTION
Stéphane Loisel1
1 Conservatoire National des Arts et Métiers (Cnam), Paris

stephane.loisel@lecnam.net
In this talk, we discuss some uncertain climate change impacts on the insurance industry. After discussing
claim worsening models and long term scenario generation best practices, we present some research challenges associated to sustainability as well as results on optimal prevention strategies.

PARALLEL SESSIONS I
Climate Risks 1
AN INTERGENERATIONAL RICE MODEL APPROACH TO ASSESS THE
IMPACT OF CLIMATE CHANGE ON SOCIAL SECURITY SYSTEMSUNDER SHARED SOCIOECONOMIC PATHWAYS
Séverine Arnold1,∗ , Ivan Fonseca Diaz1
1 University of Lausanneseverine.arnold@unil.ch (∗ corresponding author), ivanalexis.fonsecadiaz@unil.ch
Climate change is increasingly drawing the attention of research communities due to its long-term effects
on natural and social systems worldwide. The channels through which climate change can affect societies
are diverse. While physical effects can be translated into economic and life losses, the trends of societies toadapt and mitigate such physical effects can also have broader socioeconomic implications. Economic andfinancial instabilities, increasing poverty and inequality, and the collapse of health systems have been themost relevant effects studied in academic literature. Since vulnerable populations, such as the elderly andlow-income households, heavily rely on social security systems, it is critical to comprehensively analyze
future socioeconomic pathways to anticipate potential deficiencies of social security coverage and financing
mechanisms. However, despite its notable relevance, there is a noticeable lack of research on how climate
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change can affect social security systems.
This research aims to be the first approach in developing an Integrated Assessment Model (IAM) scenario analysis to derive quantitative plausible pathways on the effects of climate change on social security
systems. To this end, we extend the Regional Integrated model of Climate and the Economy (RICE) [1]to allow for intergenerational consumption and saving dynamics, thereby depicting a consistent model representation of social security systems. Using the existing framework on alternative socio-economic development narratives described by the Shared Socioeconomic Pathways (SSPs) [3, 4, 5], as well as mortality
projections derived from the International Futures (IFs) IAM [2, 6], we extend the SSP baseline scenario
representation by consistently determining consumption, savings, contributions, and retirement benefit trajectories of future generations. Our representation of social security systems for different regions around theworld, allows us to calculate optimal and actuarially fair consumption and saving allocations for active andretired populations. We use these reference paths to globally assess the adequacy and equity of contribution
rates, as well as their pertinence to ensure the sustainability of social security systems under SSPs scenarios.

References[1] Nordhaus WD (2011) Estimates of the social cost of carbon: background and results from the RICE2011 model. National Bureau of Economic Research.
[2] Hughes BB (2019) International futures: Building and using global models. Academic Press.
[3] O’Neill BC, Kriegler E, Riahi K, Ebi KL, Hallegatte S, Carter TR, Mathur R, Van Vuuren DP (2014) A
new scenario framework for climate change research: the concept of shared socioeconomic pathways.
Climatic change 122:387–400.
[4] O’Neill BC, Kriegler E, Ebi KL, Kemp-Benedict E, Riahi K, Rothman DS, Van Ruijven BJ, Van
Vuuren DP, Birkmann J, Kok K, et al. (2017) The roads ahead: Narratives for shared socioeconomic
pathways describing world futures in the 21st century. Global environmental change 42:169–180.
[5] Riahi K, Van Vuuren DP, Kriegler E, Edmonds J, O’neill BC, Fujimori S, Bauer N, Calvin K, Dellink R,
Fricko O, et al. (2017) The Shared Socioeconomic Pathways and their energy, land use, and greenhousegas emissions implications: An overview. Global environmental change 42:153–168.
[6] Sellers S (2020) Cause of death variation under the shared socioeconomic pathways. Climatic change
163(1):559–577.

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ASSESSING CLIMATE CHANCE SCENARIOS FOR VARIOUS COHORTS
OF PENSIONERS: INSIGHTS FOR NEST PENSIONS
Nick Jessop1,∗ , M. Carmen Boado-Penas2 , George Tzougas2
1 Moody’s, Insurance Solutions (United Kingdom)
2 Department of Actuarial Mathematics and Statistics, Heriot-Watt University and and the Maxwell

Institute for Mathematical Sciences, Edinburgh (United Kingdom)
nick.jessop@moodys.com (∗ corresponding author)
Pension funds are designed to offer income replacement during retirement, aligning with government policies aimed at ensuring sufficient pension provisions. Climate change impacts investments strategies, leading
investors, and pension funds to withdraw investments from carbon-intensive companies depending on climate policies.
In this paper, we forecast future returns under four different climate scenarios: ‘Current Policies’, ‘Below 2C’, ‘Net Zero 2050’, and ‘Delayed Transition’ taking into account the relationships between climatechange, economic impacts, and financial markets. Comparing different climate pathways, we show thateach current generation of contributors faces unique retirement challenges. For example, we find that, in thecase of a delayed transition, Millennials and Generation Z are likely to be most severely impacted, while
Generation X may stand to benefit.
Keywords: retirement · climate scenarios · sustainable investment · adequate pensions

STATISTICAL METHODOLOGIES TO ASSESS THE IMPACT OF CLIMATECHANGE ON INSURANCE SUSTAINABILITY. THE CASE OF
HAILSTORM RISK IN SPANISH AGRICULTURALINSURANCE-WINEGRAPESNan Zhou1 , José L. Vilar-Zanón1,∗
1 Department of Financial and Actuarial Economics & Statistics. Complutense University of Madrid, Spainzhounan@ucm.es, jlvilarz@ucm.es(∗ corresponding author)
Our research investigates the impact of climate change on hailstorm risk in the Spanish wine grape crop
insurance, utilizing the Spanish Actuarial Climate Index (SACI) [1] and advanced statistical methodologies.
Climate change, driven predominantly by human activities such as the burning of fossil fuels, has intensified
weather patterns, influencing extreme weather events that significantly affect the insurance industry. Our
study specifically focuses on hailstorm risks, which pose a unique challenge due to their localized andunpredictable nature.
Employing linear and quantile regression models, this work quantifies the influence of climate change

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on hailstorm-related insurance claims within the Spanish wine grape sector from 1990 to 2022. The SACI,
which aggregates various extreme weather variables, is used as a primary tool to measure this impact. Previous studies have shown an increase in hailstorm activity correlated with rising temperatures, but have notdirectly linked these trends to insurance claims.
Our analysis reveals a significant positive relationship between the SACI and the number of claims,
loss costs, and total losses in the sector. This correlation indicates that as the SACI increases, indicativeof worsening climate conditions, so does the financial impact on insurers. Additionally, by examining therisk in Spain’s five major wine-producing provinces, we propose a methodology for personalizing insurance
premiums and risk measures. These findings underscore the urgent necessity for the insurance industry toadapt to climate change, offering a scalable approach to risk assessment and customization of premiums andreserves.
The findings suggest that the future sustainability of the insurance sector hinges on the accurate integration of climate indices like the SACI into their risk assessment and pricing models. By quantifying thefinancial implications of climate change through such indices, insurers can better prepare for and mitigate
the economic burdens of increased hailstorm activity. This study contributes to the broader understandingof climate risk in agriculture insurance and provides a foundation for adjusting insurance practices to therealities of climate change.
Future research will focus on expanding these methodologies to other insurance lines and regions, improving the precision of risk assessments, and exploring additional risk measures to enhance the industry’s
resilience against climate-related losses. This work is vital for ensuring the sustainability of insurance markets in the face of escalating climate risks.
Acknowledgements: The research conducted by both authors was supported by the ”Ayudas a la Investigación Ignacio H. de Larramendi” grant from Fundación MAPFRE (Spain). Prof. Jose Luis Vilar-Zanóncontributed to this research while funded by grants from the Spanish Government’s Ministry of Science andInnovation, with grant numbers PID2020-115700RB-I00 and PID2021-125133NB-I00, respectively. The
database is property of AGROSEGURO S.A.

References[1] Zhou N, Vilar-Zanón JL, Garrido J, Heras Martı́nez A-J (2023) On the definition of an actuarial climate
index for the Iberian peninsula. Anales Del Instituto De Actuarios Españoles (29):37–59.
[2] Zhou N, Vilar-Zanón JL (2024) Impact Assessment of Climate Change on Hailstorm Risk in Spanish
Wine Grape Crop Insurance: Insights from Linear and Quantile Regressions. Risks (12).

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THE FRENCH ACTUARIAL CLIMATE INDEX AND ITS APPLICATION TO
PARAMETRIC INSURANCE
José Garrido1,4,∗ , Xavier Milhaud2,4 , Anani Olympio3,4
1 Concordia University, Montreal, Canada
2 Université d’Aix–Marseille, France
3 CNP Assurances, Paris, France
4 Chaire d’Excellence Digital Insurance And Long term risk - DIALog,

https://chaire-dialog.fr/
jose.garrido@concordia.ca (∗ corresponding author), xavier.milhaud@univ-amu.fr,
anani.olympio@cnp.fr
Climate change is often defined as the long–term fluctuations in climate patterns affecting the planet globally. Among its main observed effects are a rise in average temperatures in many parts of the globe, and anincrease in the frequency and severity of extreme weather events, such as floods, droughts, or wind storms.
These new climate risks are increasingly affecting the frequency and the severity of claims in different insurance branches. In order to help insurance companies predict and manage climate risks in North America,
local actuaries have created the Actuaries Climate Index™ (ACI).
Here we consider the extension of the North American ACI methodology to the climate data from
France, including its largest island, Corsica. We calculate the French Actuarial Climate Index (FACI) withdata extracted from the ERA5–Land reanalysis database, see [1]. Unlike the ACI for the United States andCanada which is calculated for 12 sub–regions, here the FACI is computed for over 10,000 cells forming the
French grid of 0.1◦ of latitude × 0.1◦ of longitude (about 123.2 km2 ). We compare the French, Australian,
Iberian and North American cases and show how the FACI tracks well the climate change of France throughthe years. Then some high-resolution FACI analyses, show the evolution for each index component, season,or region, through the years.
Finally, time permitting, we will present a possible application of FACI to the design and pricing of aparametric insurance product.
Together with the recent indices calculated for Spain and Portugal, this FACI represents one more step
towards the definition of a European index. For more details see [2].
Acknowledgement: The authors gratefully acknowledge the leadership and financial support of the Chaired’Excellence Digital Insurance And Long term risk - DIALog; see https://chaire-dialog.fr/.

References[1] Copernicus Climate Change Service (C3S) Climate Data Store (CDS) (2022). ERA5- Land hourly
data from 1950 to present. European Centre for Medium-Range Weather Forecasts. https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-land?
tab=overview.

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[2] Garrido J, Milhaud X, Olympio A (2023) On the definition of a French actuarial climate index.
Preprint. https://hal.science/hal-04491982.

Risk Management 1
STRESS TESTING WITH f -DIVERGENCES
Vaishno Devi Makam1 , Pietro Millossovich1,2,∗ , Andreas Tsanakas1
1 Bayes Business School, City, University of London
2 DEAMS, University of Trieste

pietro.millossovich.1@city.ac.uk (∗ corresponding author)
We discuss how sensitivity and (reverse and forward) stress testing of a risk management model can betackled solving an optimisation problem where the f -divergence of an alternative scenario is minimised
under some constraints. The special cases of KL- and χ2 -divergence are given special attention, and somefeatures of the general f -divergence case are investigated.

References[1] Breuer T, Csiszár I (2013) Systematic stress tests with entropic plausibility constraints. Journal of
Banking & Finance 37(5):1552–1559.
[2] Cambou M, Filipović D (2017) Model uncertainty and scenario aggregation. Mathematical finance27(2):534–567.
[3] Makam VD, Millossovich P, Tsanakas A (2021) Sensitivity analysis with χ2 -divergences. Insurance:
Mathematics and Economics 100:372–383.
[4] Pesenti SM, Millossovich P, Tsanakas A (2019) Reverse sensitivity testing: What does it take to breakthe model?. European Journal of Operational Research 274(2):654–670.

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QUANTILE REGRESSION AND PORTFOLIO REFINEMENT:ADDRESSING EXTREME BEHAVIORS IN RISK MANAGMENT
Xenxo Vidal-Llana1,∗ , Montserrat Guillén2
1 Universitat de València
2 Universitat de Barcelona

juan.j.vidal@uv.es (∗ corresponding author), mguillen@ub.edu
For any company that assumes uncertain future risk, customer segmentation is a crucial pricing strategy. For
instance, adjustments in loan interest rates, forecasts for natural disasters, and predictions of future insurance
claims all hinge on this approach. Within the realm of risk management, particular attention is directed
towards outlier behaviors, as even a small number of extreme claims can incur significant costs. Thus,
pinpointing the accurate extreme behaviors of customers and assessing their associated risks are imperative
tasks for risk analysts. Quantile regression emerges as a valuable tool for estimating the extremes of a
distribution based on multiple factors [3], similar to linear regression but focusing on specific quantiles.
Notably, estimating a spectrum of quantiles provides an approximation of the underlying distribution foreach observation, underscoring the importance of a thorough comprehension of each individual’s profile.
However, one challenge identified in existing literature is the issue of intersecting quantiles, a concern often
overlooked by traditional models [2, 1]. This limitation partly undermines the effectiveness of quantile
regression in assessing extreme behaviors. To address this, employing advanced models capable of naturallyordering extremes becomes essential [4]. We illustrate an application of such a model in identifying highrisk customers and propose strategies for portfolio refinement, particularly tailored for the operations of
insurance companies.

References[1] Cannon AJ (2018) Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes. Stochastic Environmental Research andRisk Assessment 32(11):3207–3225.
[2] He X (1997) Quantile curves without crossing. The American Statistician 51(2):186–192.
[3] Koenker R, Bassett G (1978) Regression quantiles. Econometrica: Journal of the Econometric Society
46(1):33–50.
[4] Vidal-Llana X, Salort Sánchez C, Coia V, Guillén M (2022) Non-Crossing Dual Neural Network: Joint
Value at Risk and Conditional Tail Expectation estimations with non-crossing conditions. Documentsde Treball (IREA) 2022, 15.

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A TERM STRUCTURE MODEL OF DEFAULT-FREE AND DEFAULTABLE
INTEREST RATES WITH REGIME-SWITCHING PROPERTIES:APPLICATION TO FORWARD-LOOKING STATISTICAL RISKMANAGEMENT
Yukio Muromachi
Graduate School of Management, Tokyo Metropolitan University
muromachi-yukio@tmu.ac.jp
Long-term historical data on interest rates and credit spreads can be used to identify several different
regimes, specifically, a calm regime with lower default risk and volatility and a stressed regime with higher
default risk and volatility. Regime switching models have been used not only for financial data analyses
but also for financial risk managements, mainly as scenario simulations or stress tests given highly stressed
scenarios in future. However, restricted to our knowledge, regime-switching models have not been used as
stochastic models which form the basis of the quantitative/statistical risk evaluation with the Monte Carlosimulation, except pricing derivatives. We propose a risk evaluation model of interest rate risk and credit
risk with the Markovian regime-switching property based on the framework proposed by [1], in which the
future financial risk is measured on the basis of fair (or, market-price based) valuation, and the prices andthe risks of financial instruments at present and in future are evaluated consistently on a given stochastic
financial system. Here, we discuss (1) the dynamics of the regime, interest rate, and default intensity under
the physical probability measure, and (2) the change of measure including the market prices of risks. The
dynamics under the pricing measure (for example, risk-neutral probability measure) are derived from (1)and (2), and can be used to produce the no-arbitrage term structures of default-free and defaultable interest
rates in the future.
In order to show numerical examples, we propose a tractable model. Unfortunately, the parameter
estimation of the model is not so easy because various kinds of data are necessary, and at present some
important time-series data cannot be observed yet. In order to avoid the difficulty, we introduce a few
practical assumptions in order to use other observable variables as substitutes, and propose a simple, multistep estimation method. Since the parameters estimated from the observed data do not seem bad, we usethem to do numerical simulations. Although the model looks too simple in a mathematical sense, thestochastic movements of the regime in the future generate various shapes of the future yield curves withdifferent credit ratings.
The future yield curves generated by the Monte Carlo simulation could be used for the valuation of
future cashflows derived from various assets and liabilities simultaneously, and such results would be usefulfor financial risk management, especially for asset liability management (ALM). We are preparing somenumerical examples to show in this conference; for example, the joint distribution of a bond portfolio’s
price and the volume of the non-maturity deposits on a future risk horizon, and so on. This might be
the first time to show such a theoretically consistent joint distribution, and it must give us some useful
information, at least, it would give us some images for more improved discussion of ALM. Additionally, we
can incorporate forward-looking stress scenarios from outside into our model, which implies that our model24

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might be able to connect the statistical models to the stress tests. On the other hand, in order to use such amodel appropriately, it must be necessary to pay careful attention to setting parameters and interpretation of
the results because some ad-hoc settings might have much influence on the results.
Acknowledgements: The author is grateful to Naoto Hatakeyama, Jumpei Igarashi, Prof. Toshinao Yoshiba,
and Prof. Kohta Takehara at Tokyo Metropolitan University for helpful discussions and various kinds of data
analyses. The author appreciates the research grant funded by the Grant-in-Aid for Scientific Research (C)22K04583.

References[1] Kijima M, Muromachi Y (2000) Evaluation of credit risk of a portfolio with stochastic interest rateand default processes. Journal of Risk 3(1):5–36.

INTERNAL MODELS: BACKTESTING AND SIMULATING DISTORTIONRISK MEASURES
Sören Bettels1 , Sojung Kim1 , Stefan Weber1,∗
1 House of Insurance & Institute of Insurance and Financial Mathematics, Leibniz Universität Hannover,Welfengarten 1, 30167 Hannover, Germany. www.insurance.uni-hannover.de
stefan.weber@insurance.uni-hannover.de (∗ corresponding author)
In the face of risk and uncertainty insurance companies need to measure and quantify the risk to which they
are exposed. These measurements can be used to determine the capital that is needed as a buffer against
adverse scenarios. Risk measures also help to compare portfolios or balance sheets to each other and to
guide management decisions. We focus on two issues that are important in the context of internal models: the statistical validation of the methodologies, and the efficient Monte Carlo computation of statistical
functionals, in particular measures of the downside risk.
A variety of risk measures has been suggested in the literature. Value at Risk (V@R) and Average
Value at Risk (AV@R) form the basis of various solvency regimes. An axiomatic investigation of monetaryrisk measures goes back to [1], [4], and [7], see also [5] and [6]. We present a general methodology forbacktesting and simulating an important class of risk measures, including the regulatory benchmarks V@R
and AV@R as special cases: distortion risk measures (DRMs).
DRMs are a building block in the robust representation of all distribution-based coherent risk measures.
This fact is a direct consequence of a theorem of [9]. But DRMs include many additional risk measures thatare not necessarily convex, e.g. V@R and Range Value at Risk (RV@R). DRMs are important examples ofcomonotonic risk measures, i.e., risk measures where the risks simply add up for comonotonic positions.
Our contributions are the following:
1. We propose a multinomial backtesting method for general DRMs that extends the non-randomized
AV@R-backtest of [8]. The method relies on stratification and randomization of risk levels. Our
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stratified mixture approach captures important characteristics of the DRM by weighting quantiles
according to their contribution.
2. We illustrate the performance of our methods in numerical case studies. First, we consider fixed
distributions of loss positions under the null hypothesis and under the alternatives and evaluate thesize and power of our test in this simple setting. Second, we apply our method to asset-liabilitymanagement.
3. In the special case of AV@R, our backtesting methodology deviates from previously proposed multinomial backtests suggested in [8] due to the randomization of risk levels. A numerical comparison of
the two methods shows that our approach improves the power of the backtests in all case studies.
4. For Monte Carlo simulation of DRMs in complex internal models, the stratified mixture approach canalso be combined with variance reduction techniques such as importance sampling and with machinelearning to speed up the computation of downside risk measures. The key challenge is that real-worldinternal models are analytically intractable and computationally expensive. Like black-box models,
they can only be used as oracles when variance reduction techniques are tuned. We develop suitablealgorithms and demonstrate their performance numerically.
The talk is based on the papers [2] and [3].

References[1] Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent Measures of Risk. Mathematical Finance9(3):203–228.
[2] Bettels S, Kim S, Weber S (2024) Multinomial Backtesting of Distortion Risk Measures. Submitted.
[3] Bettels S, Weber S (2024) Efficient Monte Carlo Estimation of Distortion Risk Measures and Applications. Working Paper.
[4] Föllmer H, Schied A (2002) Convex Measures of Risk and Trading Constraints. Finance and Stochastics 6(4):429–447.
[5] Föllmer H, Schied A (2016) Stochastic Finance: An Introduction in Discrete Time. 4th edition, Walterde Gruyter.
[6] Föllmer H, Weber S (2015) The Axiomatic Approach to Risk Measurement for Capital Determination.
Annual Review of Financial Economics 7:301–337.
[7] Frittelli M, Gianin ER (2002) Putting Order in Risk Measures. Journal of Banking & Finance26(7):1473–1486.
[8] Kratz M, Lok YH, McNeil AJ (2018) Multinomial VaR Backtests: A Simple Implicit Approach to
Backtesting Expected Shortfall. Journal of Banking & Finance 88:393–407.
[9] Kusuoka S (2001) On Law Invariant Coherent Risk Measures. Advances in Mathematical Economics
83–95.

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Data Science 1
THE CALCULATION OF SCR UNDER SOLVENCY II: A VINE
COPULA-GARCH APPROACH
Stefano Demartis1,∗ , Barbara Rogo1
1 Sapienza University of Rome

stefano.demartis@uniroma1.it (∗ corresponding author), barbara.rogo@uniroma1.it
In recent years, dependence patterns among various stocks have become complex. Since the global financial
crisis, many methodologies have been created to capture dependence in more flexible ways. A great partof the literature has been focused on multivariate copula as a model to capture the dependence by allowing
flexibility regarding the choice of the marginal distributions. Nevertheless, the class of multivariate copulas(mainly Elliptical and Archimedean families) is not always sufficient to capture adequate symmetry andtail dependence of multivariate data since it implies the same dependence among all pairs of variables. In
addition, the choice of bivariate copulas is huge but the set of higher-dimensional copulas is rather limited.
As specified by Czado and Nagler (2022), the class of Vine copulas tends to overcome the aforementioned
limits by using bivariate building blocks. In other words, they increase the flexibility of the model by stillallowing ”computationally tractable” estimation and model selection procedures.
This paper aims to investigate the Garch-Vine approach for two main purposes: (i) to detect the interdependencies between different stocks and (ii) to assess the Garch-Vine copula as an internal model tocompute the SCR for the equity risk. To the best of our knowledge, there are no studies that investigate thebenefits of using Garch-Vine copula as potential internal model.
(i) The model is considered for the daily log returns of multiple stocks in the London financial market.
Stocks are chosen in a way to represent different economic sectors. By looking at the results of the Vine
selection, Kendall’s Tau for each fitted pair-copula is positive, thus showing only positive correlations. The
values are not very large but enough to affirm that there are co-dependencies among stocks. By looking at
the tree graphs, we see that almost all pair copula families are selected as Student’s t copulas. This has often
been observed in financial data sets. The tree T1 of the R-Vine structure identifies Barclays stock as thecentral node in the dependence network. It means that Barclays is an important driver of the performanceof our stock portfolio and the British economy is driven by the banking sector. The estimated degree of
freedom parameters in the first tree varies between 5.5 and 11.62, thus indicating different tail behaviours ofpairs, which cannot be captured by a unique Student’s t copula because it only allows for a single degree of
freedom parameter.
(ii) Furthermore, the paper computes the SCR through the use of Vine-garch and compares it with t
Student-garch. The SCR of the portfolio has also been calculated according to the standard formula. The“pre-covid” and “covid” periods are analyzed to understand models under different economic conditions
and assess their abilities to incorporate the variation in market risk.

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References[1] Aas K (2016) Pair-copula constructions for financial applications: A review. Econometrics 4(4):43.
[2] Czado C, Bax K, Sahin Ö, Nagler T, Min A, Paterlini S (2023) Vine copula based dependence modelingin sustainable finance. The Journal of Finance and Data Science.
[3] Czado C, Nagler T (2022) Vine Copula Based Modeling. Annual Review of Statistics and Its Application 9:453–477.
[4] Nelsen RB (1999) An introduction to copulas. Springer Series and Business Media, New York.
[5] Nagler T, Krüger D, Min A (2022) Stationary vine copula models for multivariate time series. Journalof Econometrics.

INSURANCE FRAUD DETECTION VIA CLUSTERING-BASED FUZZYCLASSIFICATION ON NOISY UNBALANCED DATASETS
Oguz Koc1,∗ , Furkan Baser2 , A. Sevtap Selçuk-Kestel1
1 Middle East Technical University
2 Ankara University

oguzkoc@metu.edu.tr (∗ corresponding author), furkan.baser@ankara.edu.tr, skestel@metu.edu.tr
One of the most important challenges in overcoming the unsystematic risks in the insurance industry is
fraud detection as the expenses associated with it can be disastrous, and can increase loading on reserves
and premiums. Fraud detection may necessitate the consideration of several elements and variables due toits diverse character. Scoring systems become a valuable tool for discovering logical relationships between
several parameters, highlighting their differences, estimating risks or probabilities, and predicting the likelihood of fraud. To determine the true nature of fraud, we propose a clustering-based fuzzy classification witha noise cluster (CBFCN). This research presents a strategy based on fuzzy k-means clustering with a noise
cluster (FKMN) as a novel method for robust clustering and outlier identification. In order to determine
accurately the contributing characteristics, we combine fuzzy theory to improve the prediction capacity ofthe machine learning (ML) techniques. The implementation of CBFCN has two key components. The membership values derived from the FKMN clustering algorithm which aims to better capture the behavior ofan existing structure and identify noise (extremes) within the dataset. To illustrate how CBFCN performs
in identifying the fraud in comparison to the traditional ones, two datasets disclosing various features intheir variables are studied. Moreover, the use of noise clusters elaborates the fuzzy technique to enhance
the ML performance. The results show that the proposed CBFCN models generate promising classification
outcomes for the identification of fraud in insurance claims events. Additionally, the modification of clustering based fuzzy classification by adding noise cluster and implement its inference utilization on fraud in
automobile and health insurance aims to increase prediction ability of ML methods on imbalanced noisy
datasets. The proposed study based on work of Çelikyılmaz and Türkşen [2, 3] which utilize Logistic Regression and Support Vector Machines as the guiding implementation. Baser et. al. [1] enhance CBFC
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framework by employing Artificial Neural Network, Random Forest, Decision Tree, k-Nearest Neighbor,
Gaussian Naive Bayes, Light Gradient Boosting Machine, CatBoost, and Extreme Gradient Boosting within
the CBFC framework to measure credit default risk. In this study, we aim to improve the CBFC approach ofBaser et al. [1] by increasing robustness against noise in the clustering scheme with the FKMN frameworkand suggest CBFC with a noise.

References[1] Baser F, Koc O, Selcuk-Kestel AS (2023) Credit Risk Evaluation Using Clustering Based Fuzzy Classification Method. Expert Systems with Applications 223:119882.
[2] Celikyilmaz A, Turksen IB (2008) Enhanced fuzzy system models with improved fuzzy clustering
algorithm. IEEE Transactions on Fuzzy Systems 16(3):779–794.
[3] Celikyilmaz A, Turksen IB (2009) Modeling Uncertainty with Fuzzy Logic with Recent Theory andApplications Introduction, Springer-Verlag, Berlin.

CYBER RISK TAXONOMIES: STATISTICAL ANALYSIS OFOPERATIONAL CYBERSECURITY RISK CLASSIFICATIONS
Matteo Malavasi1,∗ , Stefan Trück2 , Gareth W. Peters3 , Pavel V. Shevchenko2 , Jiwook Jang2 ,Georgy Sofronov4
1 School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Australia
2 Department of Actuarial Studies and Business Analytics, Macquarie University, Australia
3 University of California Santa Barbara, USA
4 Department of Mathematics and Statistics, Macquarie University, Australia

m.malavasi@unsw.edu.au (∗ corresponding author), Stefan.Trueck@mq.edu.au, garethpeters@ucsb.edu,
Pavel.Shevchenko@mq.edu.au, Jiwook.Jang@mq.edu.au, Georgy.Sofronov@mq.edu.au
Cyber risk classifications are widely used in modeling of cyber event distributions, yet their effectiveness inthe out-of-sample forecasting performance remains underexplored. In this paper, we leverage on the leading industry dataset of cyber events and losses provided by Advisen to analyse the most commonly usedclassifications. We argue in favour of switching the attention from goodness of fit and in-sample predictive
performance, to focusing on the out-of sample forecasting performance. We extend threshold weighted probability scoring rules to accommodate typical features of cyber risk data, such as extreme heavy tail behavior
and heterogeneity [1, 2]. Our results indicate that business motivated cyber risk classifications appear to be
too restrictive and not flexible enough to capture the heterogeneity of cyber risk events. We investigate how
dynamic cyber risk classifiers based on risk matrix evaluation seem to be better suited in forecasting future
cyber risk losses than the other considered classifications. These findings challenge the prevailing notionof considering cyber risk as a subcategory of operational risk and suggests that cyber insurance ratemakers
should utilize cyber risk types only when modeling the cyber event frequency distribution. Our study offers
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valuable insights for decision-makers and policymakers alike, contributing to the advancement of scientificknowledge in the field of cyber risk management.

References[1] Gneiting T, Ranjan R (2011) Comparing density forecasts using threshold-and quantile-weighted scoring rules. Journal of Business & Economic Statistics 29(3):411–422.
[2] Malavasi M, Peters GW, Shevchenko PV, Trück S, Jang J, Sofronov G. (2022) Cyber risk frequency,
severity and insurance viability. Insurance: Mathematics and Economics 106:90–114.

CALIBRATION OF INSURANCE MODELS
Arthur Charpentier1,∗ , Agathe Fernandes Merchado1 , Ewen Gallic2
1 Université du Québec à Montréal (UQAM)
2 Aix-Marseille School of Economics (AMSE)

charpentier.arthur@uqam.ca (∗ corresponding author),
fernandes machado.agathe@courrier.uqam.ca, ewen.gallic@univ-amu.fr
The use of machine learning techniques poses a number of challenges in the world of insurance and actuarial
science, perhaps more epistemological than computational (and purely technical). In particular, [1] pointed
out that these techniques make it possible to further segment insurers’ portfolios, to offer more individualized
premiums, for example. How can we interpret, and use, the output of a black-box model which states that theprobability of an insured’s accident is 17.3%? Almost one hundred years ago, [8, 9] raised similar concerns:“When we speak of the ‘probability of death’, the exact meaning of this expression can be defined in thefollowing way only. We must not think of an individual, but of a certain class as a whole, e.g., ‘all insured
men forty-one years old living in a given country and not engaged in certain dangerous occupations’. A
probability of death is attached to the class of men or to another class that can be defined in a similar way.
We can say nothing about the probability of death of an individual even if we know his condition of life andhealth in detail. The phrase ‘probability of death’, when it refers to a single person, has no meaning for us
at all.”In actuarial science, the assessment of binary classifier performance traditionally centers on discriminative ability using metrics, such as accuracy. However, these metrics often disregard the model’s inherent
uncertainty, especially when dealing with sensitive decision-making domains, such as finance or healthcare.
Given that model-predicted scores are commonly seen as event probabilities, calibration is crucial for accurate interpretation. For a classifier, calibration means that the estimated class probabilities are reflective ofthe true underlying probability of the sample. Following [7], a (well-) calibrated model means that, “among
patients with an estimated risk of 20%, we expect 20 in 100 to have or to develop the event”. Probabilities
of occurrence find direct application in insurance, whether in determining mortality rates, assessing fraud
risk, or predicting the likelihood of policy terminations. Here, we illustrate the evaluation of calibration for
regression models (Logistic Regression) and ensemble methods within an insurance context. Employing
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commonly used recalibration techniques, such as local regression from [4], we aim to enhance the calibration of predicted scores. Furthermore, we extend the notion of calibration to address fairness considerations
using group-wise calibration with respect to sensitive attributes, as presented in [2] and [3].
This presentation will be based on two recent work, [5] and [6].
Acknowledgements: The first author acknowledges funding from NSERC and the SCOR Foundation for
Science.

References[1] Barry L, Charpentier A (2020) Personalization as a promise: Can Big Data change the practice of
insurance?. Big Data & Society 7(1):2053951720935143.
[2] Baumann JE, Loi M. (2023) Fairness and risk: an ethical argument for a group fairness definition
insurers can use. Philosophy & Technology 36(3):45.
[3] Charpentier A. (2024) Insurance, biaises, discrimination and fairness. Springer-Verlag.
[4] Denuit, M., Charpentier, A., & Trufin, J. (2021). Autocalibration and Tweedie-dominance for insurance
pricing with machine learning. Insurance: Mathematics and Economics, 101, 485-497.
[5] Machado AF, Charpentier A, Flachaire E, Gallic E, Hu F (2024) From Uncertainty to Precision: Enhancing Binary Classifier Performance through Calibration. arXiv 2402.07790.
[6] Machado AF, Charpentier A, Flachaire E, Gallic E, Hu F (2024) Probabilistic Scores of Classifiers,
Calibration is not Enough. arXiv (forthcoming).
[7] Van Calster B, McLernon DJ, Van Smeden M, Wynants L, Steyerberg EW (2019) Calibration: theAchilles heel of predictive analytics. BMC medicine 17(1):230.
[8] von Mises R (1928) Wahrscheinlichkeit Statistik und Wahrheit. Springer.
[9] von Mises R (1939) Probability, statistics and truth. Macmillan.

Life Insurance 1
ESTIMATION OF BIVARIATE TRANSITION RATES IN
LIFE INSURANCE
Theis Bathke1
1 Carl von Ossietzky Universiy of Oldenburg

theis.bathke@uol.de
In survival statistics, the Kaplan-Meier estimator is widely used to obtain non-parametric estimation ofsurvival functions for various modelling purposes when censoring is involved. However, this estimator can
only take into account a single event and therefore cannot capture dependencies between different events
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included in the data. There are many approaches to solve this problem, see multivariate Kaplan Meierestimators, which summarize to different estimations procedures for bivariate survival functions. Anotherimportant concept in survival analysis is the notion of recurrent events used to study recurring episodesof infection or hospitalisation. This is often modelled by introducing multistate models, which are mostly
based on modelling with Markov assumptions. In these models, estimators often target cumulative intensity
processes which provide insight into the expected number of upcoming transitions. These estimators are now
known as the Nelson-Aalen estimator for transition rates and the Aalen-Johansen estimator of transition
probabilities. The Nelson-Aalen and Aalen-Johansen estimators remain consistent on data that does notfollow the Markov assumption. However, cumulative transition rates and transition probabilities do not holdfull information about the state process without the Markov assumption, as they do not capture the temporalinterdependencies between consecutive jump events, necessary, for example, for calculating variances orhigher moments. As a solution to this problem, we have recently proposed a novel framework involving
bivariate transition rates but without suitable non-parametric estimators, see [1]. In this talk we address thelack of estimation procedures for general bivariate transition rates. We will demonstrate the relationshipto the estimation of bivariate survival functions known in survival analysis. Apart from classical survival
analysis applications bivariate transition rates are also key for the calculation of life insurance premiums orreserves of insurance contracts with special payment functions in non-Markov models. Insurance cash flows
typically include transition payments from one state to another, as well as sojourn payments for remaining in
the corresponding state. These payments can depend on past developments demanding the use of bivariate
transition rates. We show that the bivariate estimators of transition rates and probabilities can then be used
to estimate reserves for these specific path-dependent cash flows and second moments of future liabilities,
which are important for many types of risk analysis.

References[1] Bathke, T., Christiansen, M.C. Two-dimensional forward and backward transition rates. Eur. Actuar. J.
(2023). https://doi.org/10.1007/s13385-023-00363-3

A STATE-DEPENDENT APPROACH TO OPTIMAL CONSUMPTION,INVESTMENT, AND LIFE INSURANCE BY RISK-ADJUSTED UTILITIESJaime A. Londoño1 , Julie Bjørner Søe2,3,∗
1 Departamento de Matemáticas y Estadı́stica, Universidad Nacional de Colombia, Manizales, Colombia
2 Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen, Denmark
3 Mancofi A/S, 2500 Valby, Denmark

jalondonol@unal.edu.co, js@math.ku.dk(∗ corresponding author)
We derive the optimal consumption, investment, and life insurance for an agent with state-dependent preferences. To assume the state of the world impacts decision-making is natural; an agent values money con32

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forming to their social and economic context and not merely in quantitative values. We suggest an approachthat does not include more state variables nor complicate the solutions to a more intricate problem but, on
the contrary, streamlines the results.
Risk-adjusted utility reflects the idea that an agent’s preferences factor in the market’s pre-establishedrisk attitude; in other words, the agent’s preferences are state-dependent as they account for the risk in themarket before making a decision. To the authors’ knowledge, the risk-adjusted utility approach was initiallypresented by [6] within the classical [5, 4] framework. Later [1], and most recently, [3], grew this theory toinclude the possibility of life insurance and uncertain lifetime.
In this paper, we propose not exclusively to look at the risk associated with the financial world but also
to account for the risk in the actuarial world. When dealing with life insurance and including the prospectof an uncertain lifetime, the state of the world that naturally affects our decision-making is not restricted
to the financial world but includes the actuarial world. Therefore, we include the risk associated with life
insurance to enable the agent to factor in both the attitude to the risk the financial market and the insurance
market have already decided.
In the Black-Scholes market, we take cues from derivative pricing techniques, quantify the financial
worth of the payments, and compare these. Instead of evaluating the moral value of money, we compare
the risk-adjusted purchasing power, assuming the market takes a unique position on the price of the risk
associated with the financial market and the price of the risk associated with the actuarial market. We workwith a filtered probability space (Ω, F, (Ft )0≤t≤T , P) home to a market in which a financial asset and an
actuarial asset (i.e., the longevity bond) are traded. In this setting, we know from arbitrage pricing theory
that the financial value at time 0 of an F-measurable payment of u′ (t) at time t is given by E[Λ(t)u′ (t)],where Λ is a deflator that adjusts for the risk associated with both the financial world and the actuarial worlddΛ(t) = −Λ(t)(rdt +α−rdW (t) − g(t)(dN (t) − λ(t)dt)),σΛ(0) = 1.
Here, N is the process counting death of the insured, and λ is the objective mortality rate. We suggest
enclosing the risk adjusting such that the difference between the pricing and objective mortality rates isdefined by the function g > −1, as λ(t)(1 + g(t)) = λ∗ (t), interpreted as the insurance risk loading. By
including life insurance in the deflator, the financial value of payments is risk-adjusted for both financial risk
and mortality risk.
In the risk-adjusted framework, we present and interpret solutions to the optimal consumption, investment, and life insurance problem for general utility functions and CRRA (constant relative risk aversion)
power utility functions. In terms of risk-adjusted purchasing power, these solutions have a striking similarity to the log-utility optimal controls. For these solutions, we study the dynamics in terms of both nominal
values and risk-adjusted purchasing power. Therefore, we include the risk associated with life insurance toenable the agent to factor in the attitude to risk that the financial and insurance markets have already decided
upon.
Further, we explore specific corner cases to illustrate results and interpretations of the optimal controls
and their dynamics. These solutions are intuitively reasonable strategies for consumption, investment, andlife insurance under power utility and allow us to understand the framework and the solutions.

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References[1] De Los Rıos FAG, Londoño JAL, (2020) Optimal consumption, investment, and life insurance purchase: a state-dependent utilities approach. In 3rd International Conference on Computational Finance(ICCF2019) (p. 70).
[2] Londono JA, (2009) State-dependent utility. Journal of applied probability 46(1):55–70.
[3] Londoño JA (2023) Optimal Consumption and Investment with Mortality Risk and State PriceDependent Utilities.
[4] Merton R (1971) Optimal portfolio and consumption rules in a continuous-time model. Journal of
Economic Theory 3(4):373–413.
[5] Merton RC (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. The review of Economics and Statistics 247–257.
[6] Steffensen M (2001) On valuation and control in life and pension insurance. Laboratory of Actuarial
Mathematics, University of Copenhagen.

REDUCING THE GENDER GAP IN OLDER ADULT FINANCESTHROUGH REVERSE MORTGAGES
Eva Boj1,2 , Laura González-Vila1,2,∗ , Maite Mármol1,2 , Xavier Varea1,2
1 Department of Economic, Financial and Actuarial Mathematics, University of Barcelona, Diagonal 690,

08034 Barcelona, Spain
2 Observatory of European Systems of Complementary Social Pension Plans, University of Barcelona,

Diagonal 690, 08034 Barcelona, Spainevaboj@ub.edu , lgonzalezv@ub.edu (∗ corresponding author), mmarmol@ub.edu, xvarea@ub.edu
Single-person households are on the rise in developed economies [12]. Many of these households consistof individuals aged 65 and older, with women outnumbering men. This trend has raised concerns about
the economic vulnerability of older women living alone, as research shows that they are among the mostfinancially at-risk groups ([10], [11]). This observation points to a gender gap among older adults.
The gender gap is present everywhere, affecting many stages of life [4]. At work, the gender pay gap
means women generally earn less than men. This disparity carries over into retirement, resulting in lower
pensions for women and a higher risk of poverty compared to men [11]. Although several studies have
explored the gender gap in pensions among retirees ([7], [8], [5], [6], [1]), there has been little research on
the broader financial situation of older adults, including other sources of income and additional expenses
related to dependency. This study addresses this gap by examining the overall financial conditions of older
adults and focusing on the gender gap in single-person households.
As life expectancy increases [2], challenges arise not only for public pension systems but also for individuals, who face the risk of outliving their savings. Additionally, the costs associated with the final years of34

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life, often due to dependency, can be significant [3]. Reverse mortgages offer a potential solution for those
who own property but lack liquid assets [9]. This study demonstrates how reverse mortgages can reduce
the financial vulnerability of single-person households among those aged 65 and older in Spain. It also
quantifies the impact of reverse mortgages, comparing outcomes for male and female householders. Usinga lifecycle financial model that accounts for mortality and dependency, combined with stochastic simulations, the study calculates two indicators to assess economic vulnerability: the probability of illiquidity andthe mean value of lack of liquidity. These indicators also provide a way to measure the gender gap in thefinances of older adults with and without reverse mortgages.
To summarize, this study has two key contributions. First, it examines the gender gap among older
adults living alone, considering not just pensions but a broader view of income, expenses, and costs related
to dependency. Second, it shows that reverse mortgages can help reduce the gender gap by monetizing homevalues. The study confirms that a gender gap exists in single-person households, with or without reverse
mortgages, but that reverse mortgages can mitigate this gap.

References[1] A. Abatemarco, E. Lagomarsino, M. Russolillo (2023). Gender Pension Gap in EU Countries: A
Between-Group Inequality Approach. Risks 11 (3), 63. https://doi.org/10.3390/risks11030063[2] D. Atance, M.M. Claramunt, X. Varea, J.M. Aburto. (2024). Convergence and divergence in mortality: A global study from 1990 to 2030. PLoS ONE 19 (1), e0295842.
https://doi.org/10.1371/journal.pone.0295842[3] E. Boj, M.M. Claramunt, X. Varea (2020). Role of private long-term care insurance in financial sustainability for an aging society. Sustainability 12 (21), 8894. https://doi.org/10.3390/su12218894[4] A. Casarico, J. Schuetz, S. Uebelmesser (2024). Gender Inequality over the life cycle, information provision and policy preferences. Working paper. Accessed on April 15, 2024.
https://www.cesifo.org/node/79885[5] J.M. Codorniu (2021). Gender gap in retirement pensions in Spain. The impact of thematernity supplement, 83-93. In: Pensions today - economic, managerial, and social issues. Chybalski. F.; Marcinkiewicz, E. (Ed.). Łódź University of Technology Press: Łódź.
https://dx.doi.org/10.34658/9788366287938.8[6] G. Dekkers, K. Van den Bosch, M. Barslund, T. Kirn, N. Baumann, N. Kump, P. Liégeois, A. Moreira,N. Stropnik (2022). How Do Gendered Labour Market Trends and the Pay Gap Translate into theProjected Gender Pension Gap? A Comparative Analysis of Five Countries with Low, Middle andHigh GPGs. Social Science 11, 304. https://doi.org/10.3390/socsci11070304[7] European Parliament, Directorate-General for Internal Policies of the Union (2017). Gender gap in pensions: looking ahead. Publications Office of the European Union: Belgium. Accessed on April 8, 2024.
https://www.europarl.europa.eu/RegData/etudes/STUD/2017/583150/IPOL STU(2017)583150 EN.pdf[8] European Parliament, Directorate-General for Internal Policies of the Union. (2019). The gender gap in pensions in the EU. Publications Office of the European Union: Belgium.
https://doi.org/10.2861/20375

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[9] J.H. Fong, O.S. Mitchell, B.S.K. Koh (2023). Asset-rich and cash-poor: which older adults value reverse mortgages? Ageing & Society 43 (5), 1104 – 1121. https://doi.org/10.1017/S0144686X21001045[10] B.A. Morgan, I.F. Megbolugbe, D.W. Rasmussen (1996). Reverse Mortgages and the Economic Status
of Elderly Women. The Gerontologist 36 (3), 400–405. https://doi.org/10.1093/geront/36.3.400[11] OECD (2021). Pensions at a Glance 2021: OECD and G20 Indicators. OECD Publishing: Paris.
https://doi.org/10.1787/ca401ebd-en[12] E. Ortiz-Ospina (2020). The rise of living alone: how one-person households are becoming increasingly common around the world. Our work in data. Accessed on April 1, 2024.
https://ourworldindata.org/living-alone

SUBJECTIVE SURVIVAL PROBABILITIES IN LIFE INSURANCE
Apostolos Bozikas1,∗ , Apostolos Papachristos1
1 University of Piraeus

bozikas@unipi.gr (∗ corresponding author)
Subjective survival probabilities reflect individuals’ views on own future survival. This work examines theuse of subjective survival probabilities in problems of actuarial interest. More specifically, we utilize datafrom the Health and Retirement Study (HRS) for the US population, to model subjective survival probabilities and derive subjective life tables using parametric survival models. Empirical illustrations indicate thatthat these tables can lead to accurate results in pricing life insurance products.
Acknowledgement: This work has been partly supported by the University of Piraeus Research Center.

References[1] Health and Retirement Study (2018). RAND HRS Longitudinal File 2018 (V1) public use dataset. Produced and distributed by the University of Michigan with funding from the National Institute on Aging(grant number NIA U01AG009740). Available at: https://hrsdata.isr.umich.edu/data-products/rand.
[2] Peracchi F, Perotti V (2010) Subjective survival probabilities and life tables: Evidence from Europe.
Einaudi Institute for Economics and Finance (EIEF) 10:16.
[3] Perozek M (2008) Using subjective expectations to forecast longevity: do survey respondents know
something we don’t know?. Demography 45:95–113.
[4] Richards SJ (2012) A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal 2012(4):233–257.

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Risk Theory
ON A PENALTY FUNCTION IN THE ERLANG RENEWAL DUAL RISKMODEL UNDER INDEPENDENT RANDOMISED OBSERVATIONS
Renata G. Alcoforado1,2,5,∗ , Agnieszka I. Bergel2 , Rui M.R. Cardoso3 , Alfredo D. Egı́dio dos
Reis2 , Eugenio V. Rodriguez-Martinez2,4
1 Department of Accounting and Actuarial Science, Universidade Federal de Pernambuco, Recife - Brazil
2 CEMAPRE & ISEG, Universidade de Lisboa, Lisboa – Portugal
3 FCT & CMA, Universidade Nova de Lisboa, Lisboa - Portugal
4 BNP Paribas, Lisboa - Portugal
5 INSS - National Social Security Institute, Brası́lia - Brazil

alcoforado.renata@ufpe.br (∗ corresponding author), agnieszka@iseg.ulisboa.pt
rrc@fct.unl.pt, alfredo@iseg.ulisboa.pt, evrodriguez@gmail.com
We consider the dual risk model with financial application, where the random gains (or claims, using the
primal insurance risk model) occur under a renewal process. Due to the mathematical robustness of themodel we do not need to impose the usual economic condition, as shown by [2], despite the fact that theruin probability being one when the condition is not respected. We introduce a Gerber-Shiu type of penalty
function applied to the dual model and consider that randomised observations are set in place as [1] did forthe primal or classical compound Poisson insurance risk model.
We go further than these authors by studying a renewal risk process, mention in particular the Erlang(n)renewal model, and an independent observational Poisson process. Under these model ruin can only arise if
it is indeed observed, we mean, the risk process may cross downwards the zero but ruin may not happen if
it recovers before it can be observed.
We develop integral and differential equations, from which we study solutions for some cases, andparticularly solve numerically for some examples in full. We show some figures and graphs from somechosen numerical examples. We compare them, where possible, with those of [1] although worked for the
primal compound Poisson risk model.
In connection with the primal risk model, we add some final remarks and show how to use our method
to find corresponding equations to that model.
Keywords: Ruin Theory · Dual risk model · Penalty function · Randomised observations · Insurance riskmodel
Acknowledgements: Authors gratefully acknowledge support from Project CEMAPRE/REM–UIDB/
05069/2020 (CEMAPRE/REM-Centre for Applied Mathematics and Economics/Research in Economics
and Mathematics) and from Project CMA–UIDB/00297/2020 – financed by FCT/MCTES (Fundação paraa Ciência e a Tecnologia/Portuguese Foundation for Science and Technology) through national funds.

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References[1] Albrecher H, Cheung EC, Thonhauser S (2013) Randomized observation periods for the compound
Poisson risk model: the discounted penalty function. Scandinavian Actuarial Journal 2013(6):424–
452.
[2] Alcoforado RG, Bergel AI, Cardoso RM, dos Reis AE, Rodrı́guez-Martı́nez EV (2022) Ruin anddividend measures in the renewal dual risk model. Methodology and Computing in Applied Probability
24(2):537–569.

SOME APPROXIMATIONS RESULTS FOR RUIN PROBABILITIES IN THE
CLASSICAL RISK MODEL
Lazaros Kanellopoulos1
1 Department of Statistics and Insurance Science, University of Piraeus, GREECE

lkanellopoulos@unipi.gr
We study the problem of continuity in risk models. In the classical risk model with Poisson arrivals, we use
a simple technique for continuity estimation for ruin probability and the defective tail of the deficit at ruin.
Continuity inequalities are derived, which are expressed in terms of various probabilistic metrics. We also
give some numerical illustrations to investigate the accuracy of the approximations.

References[1] Beirlant J, Rachev ST (1987) The problem of stability in insurance mathematics. Insurance: Mathematics and Economics 6:179–188.
[2] Gordienko E, Vázquez-Ortega P (2016) Simple continuity inequalities for ruin probability in the classical risk model. ASTIN Bulletin 46:801–814.
[3] Politis K (2006) A functional approach for ruin probabilities. Stochastic Models 22:509–536.
[4] Rachev ST, Klebanov LB, Stoyanov SV, Fabozzi FJ (2013) The Methods of Distances in the Theoryof Probability and Statistics. Springer, New York.

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OPTIMAL RISK POLICIES AND PERIODIC DIVIDEND STRATEGIES FOR
AN INSURANCE COMPANYMark Kelbert1 , Harold A. Moreno-Franco1,∗ , Nikolai P. Pogorelov1
1 National Research University Higher School of Economics

mkelbert@hse.ru, hmoreno@hse.ru (∗ corresponding author), nppogorelov@edu.hse.ru
We study the problem of optimal risk policies and dividend strategies for an insurance company operating
under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poissonprocess. Concurrently, risk control is continuously managed through proportional reinsurance. Our analysis
confirms the optimality of a periodic-classical barrier strategy for maximizing the expected net present value
until the first instance of bankruptcy across all admissible periodic-classical strategies. [1].

References[1] M. Kelbert, H. A. Moreno-Franco, N. P. Pogorelov (2023). Optimal Risk Policies and Periodic Dividend Strategies for an Insurance Company. arXiv:2312.17131

SOME NEW APPROXIMATIONS FOR THE DENSITY OF RUIN TIME
Apostolos Papachristos1 , Konstadinos Politis2,∗
1 Department of Applied Mathematics and Physical Sciences, National Technical University of Athens,

GREECE2 Department of Statistics and Insurance Science, University of Piraeus, GREECE

apapachristos@mail.ntua.gr, kpolitis@unipi.gr (∗ corresponding author)
For the classical model of risk theory, closed formulas for the (conditional) density of ruin time Tc (Tc =T |T < ∞) are typically not available beyond the assumption of exponential claims (see, e.g., [1], [2]); here
T is the time of ruin and c the initial surplus in the surplus process. In view of this, various approximations
have beem proposed, which are typically either asymptotic in nature or require recursion [4]. Furthermore,
De Vylder approximation for the moments and the density of Tc works well for light tailed individual claim
amount distributions [3]. The objective of this study is to investigate whether distribution mixtures can besatisfactorily used to approximate the density of Tc . More specifically we investigate the approximation of
the density of Tc and ln(Tc ) using mixtures of gamma and normal distributions respectively, under different
assumptions for individual claim amount distributions. Model selection among distribution mixtures is basedon the Bayesian Information Criterion (BIC). Our results indicate that the approximation of Tc using gamma
mixtures outperforms the De Vylder approximation for different model parameters and many individual
claim amount distributions. The approach can be extended for models beyond the exponential assumption
for interarrival times.
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Acknowledgement: The second author acknowledges the financial support of the University of Piraeus
Research Center.

References[1] Dickson DCM, Waters HR (2002) The Distribution of the time to Ruin in the Classical Risk Model.
ASTIN Bulletin 32(2):299–313.
[2] Dickson DCM, Willmot GE (2005) The Density of the Time to Ruin in the Classical Poisson Risk
Model. ASTIN Bulletin 35(1):45–60.
[3] Dickson DCM, Wong KS (2004) De Vylder approximations to the moments and distribution of thetime to ruin. Australian Actuarial Journal 10(4):707–724.
[4] Cardoso RMR, dos Reis AE (2002) Recursive calculation of time to ruin distributions. Insurance:
Mathematics and Economics 30:219–230.

PARALLEL SESSIONS II
Mortality 1
MORTALITY MODELS: PRE- AND POST-COVID INSIGHTS
Şule Şahin1,∗ , Selin Özen2
1 Department of Accounting, Finance and Actuarial Science, School for Business and Society,

University of York, York, UK.
2 Department of Actuarial Sciences, Ankara University, Ankara, Turkey

sule.sahin@york.ac.uk (∗ corresponding author), ozens@ankara.edu.tr
Acknowledging the dynamic nature of global mortality trends and the significant impact of events like the
COVID-19 pandemic, this paper aims to assess the efficacy of mortality models. We compare and discuss
the performance of mortality models, both with and without jump effects, analysing their ability to capture
the mortality deterioration caused by COVID-19. Mortality models without jump effects include the LeeCarter (LC) model [5], Renshaw and Haberman (RH) model [7], and Cairns-Blake-Dowd (CBD) model [1].
In contrast, we employ mortality models with jump effects, such as the Lee-Carter model with permanent
jump effects proposed by Cox, Lin and Wang [3], transitory jump effects proposed by Chen and Cox [2],and exponential transitory jumps with renewal process effect proposed by Özen and Şahin [6]. We utilise
mortality data from Denmark, Japan, Spain, Sweden, Switzerland, and the UK obtained from the Human
Mortality Database (HMD) [4].
Given that COVID-19 is a potential cause for a jump in the mortality curve, our primary objective is to
identify the mortality models that can accurately forecast COVID deaths from 2020 onwards. To achievethis, we fit the models to pre-COVID data and forecasted the pandemic and post-pandemic years. We
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compare the performance of the models considering both in-sample and out-of-sample forecasting, analyse
the estimated parameters, and focus specifically on the time-dependent parameter in which explicit jumps
were added for the mortality jump models discussed. Furthermore, we present the valuation of mortalityrelated insurance products such as term life annuity and life insurance, using both the jump-free and jumpmodels calibrated for pre- and post-COVID data.
One significant observation is that the fit and forecast performance of mortality models, whether including jump effects or not, heavily depends on the specific country, time, and age period to which they are
fitted. Despite in-sample prediction and model fitting statistics indicating better results for jump models, theforecasting of COVID deaths and death rates for some countries does not support this conclusion. However,overall, when considering the accuracy of true forecasts for all six countries, jump models outperform byproviding the most accurate forecasts in a majority of cases. Notably, the RH model, offering the most accurate forecasts for a significant portion of cases, might offer insights into future improvements in mortality
jump modelling, particularly in considering the age/cohort pattern of the jumps.
Another notable observation concerning the forecasts is that the potential jump induced by the COVID19 pandemic, if it occurred, appears more pronounced in older age groups. This trend is reflected in theperformance of jump models tailored specifically for these demographics. However, it is crucial to recognisethat the sensitivity of the results may vary based on factors such as altering the age range, exploring genderspecific data, or considering a different time frame for analysis.
Taking into account the valuation findings for term life annuities and life insurance, post-COVID calibration results in higher mortality forecasts for all countries except Japan. This suggests a pandemic-induced
jump and, consequently, lower present values for life annuities and higher present values for life insurance.
Jump models exhibit similar present values forming clusters, whereas jump-free models lack such patterns.
The CBD model consistently produces larger confidence intervals across all countries.
This conference paper is based on the research published in Risks ([8]).

References[1] Cairns AJG, Blake D, Dowd K (2006) A Two-Factor Model for Stochastic Mortality with Parameter
Uncertainty: Theory and Calibration. Journal of Risk and Insurance 73:687–718.
[2] ChenH, Cox SH (2009) Modeling Mortality with Jumps: Applications to Mortality Securitization.
Journal of Risk and Insurance 3:727–751.
[3] Cox SH, Lin Y, Wang SS (2006) Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization. Journal of Risk and Insurance 73:719–736.
[4] Human Mortality Database. www.mortality.org.
[5] Li RD, Carter LR (1992) Modeling and Forecasting U.S. Mortality. Journal of the American Statistical
Association 87:659–671.
[6] Özen S, Şahin Ş (2020) Transitory Mortality Jump Modeling with Renewal Process and Its Impact on
Pricing of Catastrophic Bonds. Journal of Computational and Applied Mathematics 376:1–15.
[7] Renshaw AE, Haberman S (2006) A Cohort-Based Extension to the Lee-Carter Model for Mortality
Reduction Factors. Insurance: Mathematics and Economics 38:556–570.

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[8] Şahin Ş; Özen S (2024) A Quantitative Comparison of Mortality Models with Jumps: Pre- and PostCOVID Insights on Insurance Pricing. Risks 12(3):53. https://doi.org/10.3390/risks12030053

MORTALITY FORECASTING VIA MULTI-TASK NEURAL NETWORKS
Luca De Mori1,∗ , Steven Haberman1 , Pietro Millossovich1,2 , Rui Zhu1
1 Bayes Business School
2 Università degli Studi di Trieste

luca.de-mori@bayes.city.ac.uk (∗ corresponding author), s.haberman@city.ac.uk,
pietro.millossovich.1@city.ac.uk, Rui.Zhu@city.ac.uk
In the last decades, analysing the progression of mortality rates has become highly significant in both public
and private pension schemes and the life branch of insurance companies. Traditionally, the tools used inthis field were based on stochastic and deterministic approaches that allow extrapolating mortality rates
beyond the last year of observation. More recently, new techniques based on machine learning have been
introduced as alternatives to traditional models, giving practitioners new opportunities. Among these, neuralnetworks play an important role due to their computation power and flexibility to treat the data without
any probabilistic assumption. In our research, we apply multi-task neural networks, whose approach isbased on leveraging useful information contained in multiple related tasks to help improve the generalized
performance of all the tasks [2], to forecast mortality rates. The architecture of these multi-task neuralnetworks also depends on clustering based on previous mortality experiences of the populations. Finally,
we quantitatively compare the performance of multi-task neural networks to that of stochastic models andexisting single-task neural networks [1] on mortality data of ten countries from the HMD.

References[1] Richman R, Wüthrich M (2021) A neural network extension of the Lee–Carter model to multiple
populations. Annals of Actuarial Science 15(2):346–366.
[2] Crawshaw M (2020) Multi-task learning with deep neural networks: A survey. arXiv:2009.09796.

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IMPACT OF HEAT WAVES ON MORTALITY: EXTENSION OF
LONGEVITY MODELS TO ACCOUNT FOR GLOBAL WARMING
Xavier Milhaud1,∗ , José Garrido2 , Jean-Luc Gouthon1
1 Aix-Marseille Université
2 Concordia University

xavier.milhaud@univ-amu.fr (∗ corresponding author), jose.garrido@concordia.ca,
abiodun.jean-luc.gouthon@univ-amu.fr
Mortality and prospective mortality models, also known as longevity models, have long been studied in theactuarial community. However, the vast majority of these models focus on univariate modeling, country bycountry. In this work, we introduce a new multivariate approach, in the same spirit as the multi-population
extension of the Lee-Carter model ([3]) or other recent works (see [1] and [2] among many others). This
notably allows for the consideration of both temporal mortality dynamics and interactions that may exist
between countries. To achieve this, we introduce an approach based on a combination of neural networks
with memory. This new model is tested on real data from the Human Mortality Database, and the results arecompared to the best competing models in the literature.

References[1] Wang P, Pantelous AA, Vahid F (2023) Multi-population mortality projection: The augmented common factor model with structural breaks. International Journal of Forecasting 39(1):450–469[2] Lam KK, Wang B (2023) Multipopulation mortality modelling and forecasting: the weighted multivariate functional principal component approaches. Journal of Applied Statistics 50(15):3177–3198.
[3] Li N, Lee R (2005) Coherent mortality forecasts for a group of populations: An extension of the
Lee-Carter method. Demography 42:575–594.

Nonlife Insurance Mathematics 1
HMM-BASED COX MODELS FOR IBNR RESERVING
Hassan Abdelrahman1,∗ , Andrei Badescu1 , Sheldon Lin1
1 Department of Statistical Sciences, University of Toronto

hassan.abdelrahman@mail.utoronto.ca (∗ corresponding author)
Accurate loss reserving in Property and Casualty (P&C) insurance is essential for maintaining financial
stability, ensuring regulatory compliance, and managing risk effectively. This project focuses on Incurred
But Not Reported (IBNR) reserving, a particularly challenging aspect of loss reserving due to the unknown
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nature of these claims. Traditional reserving methods, such as the chain ladder and Bornhuetter-Ferguson
models, aggregate historical claims data to estimate reserves but face significant limitations. These macrolevel models often lose valuable insights into individual claims, suffer from high parameter uncertainty due
to limited aggregated data, and may introduce biases under certain conditions.
To overcome these limitations, micro-level models that utilize individual claim data have been proposed. Notably, early stochastic loss reserving frameworks at the individual claim level were developed
using marked non-homogeneous Poisson processes (NHPP). Models based on NHPP often fail to accountfor dependencies among individual claims and environmental variations affecting the entire portfolio. Addressing these issues involves incorporating a temporal dependence structure into the claim arrival processmodel, achievable by transitioning to a Cox model. Notable research in this direction includes the utilization of a shot noise Cox process and hidden Markov model (HMM) to model the claim arrival process forthe entire portfolio, overlooking policy-holder information that should enhance the accuracy of the different
components within the model.
In this study, we introduce a novel micro-level Cox model that addresses these shortcomings by incorporating a hidden Markov model (HMM) to capture temporal dependencies and environmental variations.
Our model offers flexibility by allowing analysis at various levels of granularity, such as policyholder-level,line of business-level, or portfolio-level, thereby providing a comprehensive framework for analyzing claim
arrival patterns. The HMM governs the claim arrival processes across different units within the portfolio,
with the claim arrival intensity for each policyholder influenced by both external factors and individual risk
attributes.
Furthermore, our approach integrates the modeling of reporting delays and claim frequencies within acohesive discrete-time framework. The change in direction from the continuous-time to the discrete-timeframework allows us to capture the intricate interplay between claim occurrence and reporting behavior,
which is often overlooked in traditional continuous-time models. By addressing the complexities associatedwith right-truncated reporting delays and the interdependence of claim frequency and reporting delay, ourmodel provides a more accurate representation of real-world claim arrival processes.

ONE-YEAR AND ULTIMATE CORRELATIONS IN DEPENDENT CLAIMSRUN-OFF TRIANGLESŁukasz Delong1 *, Marcin Szatkowski2
1 University of Warsaw, Faculty of Economic Sciences
2 Cogitato Foundationl.delong@uw.edu.pl (*corresponding author), marcin.szatkowski@cogitato.pl
We investigate bottom-up risk aggregation applied by insurance companies facing reserve risk from multiplelines of business. Since risk capitals should be calculated in different time horizons and calendar years,
depending on the regulatory or reporting regime (Solvency II vs IFRS 17), we study correlations of ultimate
losses and correlations of one-year losses in future calendar years in lines of business. We consider amultivariate version of a Hertig’s lognormal model, see e.g. in [1] and [2], and we derive analytical formulas
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for the ultimate correlation and the one-year correlations in future calendar years. Our main conclusion isthat the correlation coefficients which should be used in a bottom-up aggregation formula depend on the time
horizon and the future calendar year where the risk emerges. We investigate analytically and numericallyproperties of the ultimate and the one-year correlations, their possible values observed in practice and theimpact of misspecified correlations on the diversified risk capital.
Acknowledgement: The first version of this paper was financially supported with grant NCN
2018/31/B/HS4/02150.

References[1] Merz M, Wüthrich MV, Hashorva E (2012) Dependence modelling in multivariate claims run-off triangles. Annals of Actuarial Science 7:3–25.
[2] Wüthrich MV (2015). Stochastic Claims Reserving Manual: Advances in Dynamic Modeling. SSRN.

ADVANCING ACTUARIAL CLAIM MODELING: ADDRESSINGUNOBSERVED RISK FACTORS WITH A HMM
Mustafa Asım Özalp1,∗ , Şule Şahin2 , Kasirga Yildirak1
1 Department of Actuarial Sciences, Hacettepe University
2 Department of Accounting, Finance and Actuarial Science, School for Business and Society,

University of Yorkasimozalp@hacettepe.edu.tr (∗ corresponding author), sule.sahin@york.ac.uk, kasirga@hacettepe.edu.tr
The primary objective of insurance companies is to protect policyholders against potential losses in exchange
for a specified premium [1]. To achieve this, it is essential to charge a fair premium and maintain adequate
capital and reserves. Accurate prediction of claim frequency and amounts, both individual and aggregate,is crucial as it directly impacts pricing and reserving strategies. Over the past four decades, Generalized
Linear Modeling (GLM) has become vital for actuaries in rate-making, pricing, and reserving due to its
flexible framework in parameter and model selection [2, 3].
Heterogeneity in statistical modeling arises from deviations due to unobservable risk factors. In claim
modeling, random effects represent unobserved risk factors, while fixed effects represent observed ones.
The Generalized Linear Mixed Model (GLMM) is a recognized approach for managing this heterogeneity,
though random effects can increase the correlation variance of the dependent variable [4, 3]. Studies havealso explored heterogeneity in credibilit or tariff models, often focusing on time-varying heterogeneity overunobservable risk factors, using extensions like the state-space model (SSM) [5, 6].
Serial correlation in claim modeling refers to the relationship between claim frequencies or severities
and their lagged versions, which can increase the variance of demand frequencies. GLMMs and time series
approaches in longitudinal settings have been proposed to manage this serial correlation [7, 3].

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This study aims to demonstrate, through extensive validation, that the proposed method outperforms
existing models in addressing actuarial loss function challenges. The new approach enhances adaptability,
flexibility, accuracy, and applicability, potentially uncovering complex hidden risk factors. Simulation studies and real-life dataset applications were used to evaluate the model’s performance. The primary goal is toillustrate how the model effectively represents heterogeneity from unobserved risk factors.
Our findings reveal that heterogeneity from unobserved risk factors is represented by three discrete hidden states in the analyzed dataset. Extensive validation confirms that the proposed method surpasses existingmodels in handling actuarial claims modeling complexities. Real-life examples show that the new method
yields superior results by effectively representing heterogeneity and serial correlation based on unobservablerisk factors. This innovative approach offers robust solutions to traditional actuarial claim model challenges,
significantly advancing actuarial science

References[1] Rocca G (2019) Predictive methods for calculating the non-life insurance premium (Doctoral dissertation, Politecnico di Torino).
[2] Renshaw AE (1994) Modelling the claims process in the presence of covariates. ASTIN Bulletin: theJournal of the IAA 24(2):265–285.
[3] Denuit M, Trufin J (2019) Effective statistical learning methods for actuaries, Vol.795. Springer, Berlin.
[4] McCulloch CE, Searle SR, Neuhaus JM (2001) Generalized, linear, and mixed models, Vol.325. John
Wiley & Sons, New York.
[5] Pinquet J, Guillen M, Bolance C (2001) Allowance for the age of claims in bonus-malus systems.
ASTIN Bulletin: The Journal of the IAA 31(2):337–348.
[6] Pinquet J (2020). Poisson models with dynamic random effects and nonnegative credibilities per period. ASTIN Bulletin: The Journal of the IAA 50(2):585–618.
[7] Avanzi B, Wong B, Yang X (2016) A micro-level claim count model with overdispersion and reporting
delays. Insurance: Mathematics and Economics 71:1–14.

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Risk Management 2
A PUBLIC DIRECTORS AND OFFICERS LIABILITY RISKQUANTIFICATION MODEL BASED ON GENERALIZED LINEAR
MODELS
Andrei Craciunescu1,∗ , Matthias Scherer1 , Emma Iversen1
1 Technical University of Munich, chair of mathematical finance, Garching, Bavaria, Germany

andrei.craciunescu@tum.de (∗ corresponding author), scherer@tum.de, emma.iversen@tum.de
Directors and Officers (D&O) insurance has become essential to corporate governance, protecting against
the financial consequences of lawsuits, regulatory actions, and other liabilities [2]. However, quantifying
D&O risk is challenging, complicated by the scarcity of historical data and the complexity of the risk factors
involved [3]. The vast majority of literature on D&O insurance explores a qualitative approach. Meanwhile,
those adopting a quantitative perspective primarily focus on the impact of D&O insurance on the financial
market [1]. This paper proposes a frequency and severity model for D&O risk quantification based on Generalized Linear Models (GLMs). The approach is estimated on historical data from US-based companies
obtained from different sources and incorporates different industry sectors and company sizes. The analysis is divided into two parts. In the first one, we investigate D&O claims frequency modelling. In thesecond part, we investigate the modelling of the severity of claims. For the frequency, we compare models
based on the Negative Binomial, Poisson, and mixed Poisson distributions to evaluate which model best
fits the data. Our findings reveal that the Negative Binomial outperforms the others for our dataset. This
information is incorporated into the GLM framework to model the frequency of D&O claims with different
covariables. In the severity analysis, we used Log-normal models for the entire dataset and a combinationof Log-normal and Generalized Pareto Distribution (GPD) models to distinguish between attritional losses
and the tail events. Our investigation revealed that the log-normal distribution provides the best trade-off
between goodness-of-fit and complexity for the data. Using the available covariables, we captured the heterogeneity and complexity of severity modelling using the GLM framework. These results provide insights
for insurers and policymakers, aiding in developing more accurate risk assessment and pricing strategies.

References[1] Chen L, Micah S, Rui W, Hong Z (2011) Directors’ and Officers’ Liability Insurance and Loan Spreads.
Journal of Financial Economics 110(1):37–60.
[2] Nelson AR (2010) Directors and Officers Liability Insurance – The Basics. Wallace Folick LLP.
[3] Next Move Strategy Consulting (2022) Directors and Officers (D&O) Insurance Market by Coverage,
and End User - Global Opportunity Analysis and Industry Forecast, 2022-2030. Report.

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OPTIMAL INVESTMENT AND SUSTAINABLE TAXATION
Ralf Korn1,2 , Ajla Nurkanović1,∗
1 Department of Mathematics, RPTU Kaiserslautern-Landau, Kaiserslautern 67663, Germany
2 Department of Financial Mathematics, Fraunhofer ITWM, Kaiserslautern 67663, Germany

korn@mathematik.uni-kl.de, nurkanov@rhrk.uni-kl.de (∗ corresponding author)
Since August 2022, regulatory requirements mandate that customers be queried about their interest (demand) in sustainable investment upon initiating a pension contract. Consequently, providers must anticipate
the need to furnish appropriate investment opportunities. Moreover, they face the challenge of effectively
managing the inherent risks and opportunities associated with these assets across their entire portfolio. Motivated by that, in [1] we especially looked at possible consequences for optimal portfolio decisions of a life
insurer and suggested modeling approaches for the evolution of the demand and the sustainability ratings
for sustainable assets. We solved various portfolio problems under sustainability constraints explicitly andsuggested further research topics. As a special feature for a life insurer, we particularly looked at the role of
the actuarial reserve fund and the annual declaration of its return.
Building further on that work, we now explore the nuanced interplay between unconstrained portfolio optimization and sustainability constraints (the customers’ demands). Specifically, we investigate thescenario where a sustainable optimal portfolio with demand deviates from a corresponding unconstrained
portfolio. We pose the question: What adjustments to the portfolio’s vector of mean rates of stock returns,
symbolized by the parameter b, are necessary to ensure that the unconstrained optimal portfolio remains sustainable? We introduce this ”hidden tax” on the portfolio as an aim to induce market behavior that supports
sustainability. We derive the formulae for b̃, the adjusted b, under two distinct utility functions: logarithmic
and power utility. Deriving the derivatives of b̃i w.r.t. the power utility parameter γ and the demand D, weanalyze the changes in monotonicty w.r.t. these parameters. Further, we conduct numerical analysis and parameter sensitivity testing in a two-dimensional portfolio setting, comprising two risky assets and a risklessasset. Throughout our analysis, we maintain constant ratings and demand over time. We explore scenarios
involving both independent and correlated assets, assessing the impact on portfolio behavior under the two
utility functions. Additionally, we consider the cases with and without the max offer condition, where themax offer condition means the demand D is not higher than the maximum available rating of the portfolio
assets.
Our findings, both theoretical and numerical, reveal unforeseen dynamics arising from sustainability
demands. The monotonicities of b̃i w.r.t. γ and D are dependent on the relationship between R0 (rating of
the riskless component) and Ri (rating of the asset i), whether R0 is greater, equal to, or smaller than Ri .
Thus, under power utility, we observe instances where higher γ parameters do not consistently correspondto increased investment in risky assets. Additionally, whether higher demand D for sustainability imposes
higher b̃i or not, again depends on that relationship between R0 and Ri . These unexpected behaviors underscore the complexity introduced by sustainability constraints, even in seemingly straightforward scenarioswith a two-dimensional portfolio. On the other hand, portfolios lacking the maximum offer condition tend
to incur significantly more negative positions in assets. Given our aim to reduce short selling of sustainableassets, which could undermine efforts to advance environmentally responsible practices, the importance of48

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implementing the maximum offer assumption becomes evident.
Our study highlights the intricate interplay between sustainability considerations and portfolio optimization, emphasizing the need for further research in this domain. Already for a two-dimensional problem andconstant ratings and demand, our results underscore the challenges inherent in integrating sustainability
constraints into portfolio management practices.

References[1] Korn R, Nurkanovic A (2023) Optimal portfolios with sustainable assets: aspects for life insurers.
European Actuarial Journal 13(1):125–145.

INSURANCE PRODUCT DESIGN AND ATTRIBUTES RELATING TO
SOCIAL AND ENVIRONMENTAL SUSTAINABILITY: A SYSTEMATIC
REVIEW ON RETAIL MOTOR INSURANCE
Kristien Doumen1 , Luc Van Liedekerke1 , Jenna Vergeynst1 , Laila El Meknouzi1 , Femke Snels1
1 University of Antwerp, Faculty of Business and Economics, Department of Management

kristien.doumen@uantwerpen.be, luc.vanliedekerke@uantwerpen.be, jenna.vergeynst@uantwerpen.belaila.elmeknouzi@student.uantwerpen.be, femke.snels@student.uantwerpen.be
Insurance companies play a vital role in managing societal risks and providing financial resilience. In lightof this critical role, this systematic review examines the intersection of insurance products with environmental and social themes, focusing on retail motor insurance. The aim of the review is to map the choicesthat an insurer can make in insurance product design and attributes relating to social and environmental
sustainability.
This review builds upon existing reviews that outline sustainability within an insurance context, including [1], [2], [3], [4] and [5]. This review contributes to the field by concentrating on insurance productdevelopment and focussing on one type of insurance line. This increases the granularity of insights into how
particular design choices impact specific environmental and social themes. Thereby, we respond to the callof [5] for more detailed sustainability roadmaps and implementation criteria for practice. Moreover, thisresearch addresses the described gap on research on social factors and the integration of environmental andsocial factors into risk management and underwriting.
Through a systematic search of Web of Science and Scopus, fifty relevant articles were identified andanalysed using descriptive within- and cross-case analysis, employing thematic analysis. The resultant
sample exhibits significant diversity in research domains and methodologies, albeit with a notable bias
towards the Western World and Anglosphere.
The preliminary findings have identified the environmental themes: emissions, noise pollution, energy
consumption, waste and materials. Social themes are safety, privacy, accessibility, fairness, discrimination,affordability, transparency, health and congestion. While environmental themes are transparent and defined,49

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social themes are more overlapping and intertwined. Literature focuses on various designs of Usage-Based
Insurance (UBI), particularly relevant for environmental sustainability. Some social sustainability themes
require distinguishing between third-party and comprehensive motor insurance, and between at-fault andno-fault products.
The review reveals how the attributes of motor insurance, underwriting, pricing, acceptance and cancellation, claim settlement, services and terms and conditions of motor insurance, relate with these societal
themes. These granular insights include how rating factors like mileage, emissions factor of fuel type or
health of policyholder relates to themes like emissions, congestion, privacy and safety; how adopting salvaged parts in claim settlement is integrated in terms and conditions and impacts pricing in order to support
waste reduction; how pricing and cross subsidies relate to affordability of insurance and to different conceptions of fairness; how hydrogen vehicles are beneficial for emissions, but increase physical accident
risk. The relationship between motor insurance product design and attributes and social and environmental
sustainability is visualized in a conceptual model.
This review enhances comprehension of sustainability within the insurance industry, elucidates mechanisms for change in the industry, and delineates nuanced sustainability themes. Its relevance extends to bothacademics and practitioners.
Acknowledgements: We acknowledge the financial support from a Multinational Insurance Company andthe guidance of sustainability professionals at this insurer as well as the Belgian Insurance Association. Our
gratitude extends to colleagues for their collaboration on the sample selection and screening, as well as thedata analysis. We also wish to thank prof. dr. Paula Jarzabkowski and dr. Konstantinos Chalkias for theirconstructive feedback during the process.

References[1] Mills E (2009) A Global Review of Insurance Industry Responses to Climate Change. The Geneva
Papers on Risk and Insurance. Issues and Practice. 34(3):323–359.
[2] Gatzert N, Reichel P, Zitzmann A (2020) Sustainability risks and opportunities in the insurance industry. Zeitschrift für die gesamte Versicherungswissenschaft 109(5):311–331.
[3] Sasidharan S, Ranjith VK, Prabhuram S (2021) Insurer’s Role in Intensifying Environmental Sustainability and Social Development. J. Fin. Bank. Review 6:126–133.
[4] Stricker L, et al. (2022) Green Insurance: A Roadmap for Executive Management. Journal of Risk and
Financial Management 15, DOI: 10.3390/jrfm15050221.
[5] Aburto Barrera LI, Wagner J (2023) A systematic literature review on sustainability issues along thevalue chain in insurance companies and pension funds. European Actuarial Journal 13(2):653–701.

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ASSET-LIABILITY MANAGEMENT WITH LIQUID AND FIXED-TERM
ASSETS
Yevhen Havrylenko1
1 Department of Mathematical Sciences, University of Copenhagen, Denmark

yh@math.ku.dk
Insurance companies and pension funds have asset-allocation processes that may involve multiple risk management constraints due to liabilities. Furthermore, the investment universe of such institutional investors
often contains assets with different levels of liquidity, e.g., liquid stocks and illiquid investments in infrastructure projects or private equity. Therefore, we propose an analytically tractable framework for economic agents who maximize their expected utilities of terminal portfolio value by choosing investmentconsumption strategies subject to lower bound constraints on both intermediate consumption and the terminal value of assets, some of which are liquid, while others are fixed-term. For institutional investors suchas insurance companies consumption can be interepreted as payments to policyholders and/or dividends toshareholders.
In our faremework, we model fixed-term assets as in [1] and extend that paper by adding consumption
and by integrating risk-management constraints. Combining the generalized martingale approach with theideas from [2] and [3], we derive optimal decisions in our framework.
In our talk, we present the key building blocks of our framework and demonstrate how to derive optimal
investment-consumption strategies. At the end of the talk, we consider a numerical study where we analyze
optimal strategies from the insurance economics perspective.

References[1] Desmettre S, Seifried FT (2016) Optimal asset allocation with fixed-term securities. Journal of Economic Dynamics and Control 66:1–19.
[2] Korn R (2005) Optimal portfolios with a positive lower bound on final wealth. Quantitative Finance5(3):315–321.
[3] Lakner P, Nygren LM (2006) Portfolio optimization with downside constraints. Mathematical Finance16(2):283–299.

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Ratemaking
WEEKLY DYNAMIC MOTOR INSURANCE RATEMAKING WITH A
TELEMATIC SIGNALS BONUS-MALUS SCORE
Juan Sebastián Yánez1,∗ , Montserrat Guillén1 , Jens Perch Nielsen2
1 University of Barcelona
2 City, University of London

yanez.juansebastian@gmail.com (∗ corresponding author), mguillen@ub.edu, Jens.Nielsen.1@city.ac.uk
Telematic data has given researchers and actuaries a new perspective on how motor insurance premiums
can be calculated. Through vast amounts of information collected from GPS devises in either the car or thecellphone of drivers, a clearer picture of the driving profile of the client can be obtained. Ideally an insurer
would be able to determine premiums based on driving skill and habits, leading to better risk identification,
as shown by [3]. Thus, not only reducing adverse selection for the insurer but also motivating the client todrive more securely as safe driving is encouraged via premium reductions. As such, there is a real incentive
for the insurer to implement pay-how-you-drive (PHYD) pricing schemes in order to take full advantage ofthe telematic data collected.
Although telematic information has proven to be powerful tool to identify risks, actual dynamic pricing
methods using this information in real time, such as [1] and [2], are scarce. Indeed, there are two maindifficulties when incorporating this data in a pricing scheme. First, unlike traditional rating factors, which
are known before the coverage period is observed, this data is collected as the client drives. Thus, the insurer
either has to charge a premium after the client has driven or predict future telematic events based on present
information. Second, including telematic information into models, often leads to big data difficulties as
there could be a very large amount of data collected. In our presentation we aim to provide a pricing schemethat tackles these two challenges.
We focus our research on ”near-miss” events (also known as telematic signals, risky events or nearclaims in the literature). Commonly, in the rate-making literature a near-miss is more broadly defined as apunctual event that has an effect on claim occurrence. This article focuses on two events: accelerations andbraking events, given that the positive correlation between these events and accident risk is well documented
in the literature (see [4]).
The advantage of including near-misses in a pricing scheme is twofold. The first advantage is that nearmiss events occur more frequently than actual claims. Depending on the exact definition of a near-miss, theratio between near-misses and actual claims could easily be one to a hundred. This allows us to turn froma low frequency setting to a more dynamic one, for example from a yearly premium structure to a weekly
one. The second advantage is that the driving profile of a client can be determined in simpler terms. The
idea being to focus only on a handful of near-miss events rather than broader telematic data. This allows
the insurer to circumvent potential difficulties in the implementation of large quantities of data. In addition,
they could share and explain the premium increases to their clients in a more transparent way.
In our paper we suggest a pricing scheme that allows the insurer to dynamically benefit from data provided by previous near-miss counts to determine a more accurate premium before telematic data is collected.
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Indeed, by predicting the near-miss count to be observed on a given period based on past information, a classical pricing structure can be implemented. The idea being to combine traditional risk factors and near-misspredictions to charge a premium at the beginning of a covered period. Hence, our approach allows the insurer to charge premiums preemptively (as classical approaches would) while benefiting from past telematic
information. In other words, new telematic data impacts the total premium charged in two ways. First,
it allows for better prediction of future near-miss events and thus impacts the preemptive premium for anunobserved period. Second, it allows the insurer to adjust the previously charged premium through theinclusion of observed telematic data.
In terms of the near-miss predictions used in our pricing scheme, we chose to adapt a Bonus-Malus
System (BMS). We believe this is a natural implementation. Both our near-miss pricing scheme and abonus-malus approach share a similar goal of rewarding (or punishing) drivers based on the occurrence of
events (or lack thereof). Furthermore, most bonus-malus scores are designed for claim counts, which likenear-misses, are punctual events. It is worth noting that, with a higher frequency in terms of observations,the bonus-malus structure can be more dynamic as we can allow it to change on a shorter time span (itsvalue may change on a weekly basis rather than on a yearly basis).
Acknowledgements: Juan Sebastián Yánez thanks the financial support from the Fonds de recherche duQuébec (FRQ) (grant B3X-346658). Montserrat Guillén thanks ICREA Academia and support received
from Spanish Ministry of Science and Innovation grants PID2019-105986GB-C21 and MCIN/AEI/10.13039/501100011033 TED2021-130187B-I00.

References[1] Guillen M, Nielsen JP, Pérez-Marı́n AM (2021) Near-miss telematics in motor insurance. Journal of
Risk and Insurance 88(3):569–589.
[2] Henckaerts R, Antonio K (2022) The added value of dynamically updating motor insurance prices withtelematics collected driving behavior data. Insurance: Mathematics and Economics 105:79–95.
[3] Verbelen R, Antonio K, Claeskens G (2018) Unravelling the predictive power of telematics data in
car insurance pricing. Journal of the Royal Statistical Society Series C: Applied Statistics 67(5):1275–
1304.
[4] Ma YL, Zhu X, Hu X, Chiu YC (2018) The use of context-sensitive insurance telematics data in auto
insurance ratemaking. Transportation Research Part A 113:243–258.

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CONVEX AND LORENZ ORDERS UNDER BALANCE CORRECTION INNONLIFE INSURANCE PRICING
Michel Denuit1 , Julien Trufin2
1 Institute of Statistics, Biostatistics and Actuarial Science - ISBA, Louvain Institute of Data Analysis andModeling - LIDAM, UCLouvain, Louvain-la-Neuve, Belgium
2 Department of Mathematics, Université Libre de Bruxelles (ULB), Brussels, Belgium

By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail toachieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average
self-financing. Balance correction has been proposed as a way to make any candidate premium autocalibrated with the added advantage that it improves out-of-sample Bregman divergence and hence predictive
Tweedie deviance. In this talk, we prove that balance correction is also beneficial in terms of concentration
curves and we derive conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing
predictors in the convex order.

MARKET-BASED INSURANCE RATEMAKING
Pierre-Olivier Goffard1,∗ , Gareth W. Peters2 , Pierrick Piette3,2
1 Université de Strasbourg, Institut de Recherche Mathématique Avancée, Strasbourg, France
2 University of California Santa Barbara, Department of Statistics and Applied Probability, Santa Barbara

CA 93106-3110, USA
3 Seyna, 10 Rue du Faubourg Montmartre 75009 Paris

goffard@unistra.fr (∗ corresponding author), garethpeters@ucsb.edu, pierrickpiette@gmail.com
Modern insurance pricing relies on predictive modeling methods to ensure that premiums accurately reflect
the average cost of claims. However, when an insurance company enters a new market without historical
data, conventional predictive modeling tools fail, necessitating innovative solutions.
An alternative is to analyze market data from competitors’ rates for similar insurance policies. Our approach
uses this market data to develop a methodology for determining suitable commercial premiums based on
observed rates. We use pet insurance as a case study, collecting data on premiums by specifying rating
factors such as species, breed, age, and gender.
Within a specific risk class, the total claim amount X is a positive random variable. Insurers offer coveragefor g(X) < X in exchange for a premium, calculated as the pure premium p = E[g(X)]. The commercial
premium π = f (p) > p is related to the pure premium by a loading function f . Given insurance quotes

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D = {π1 , . . . , πn }, such that
πi = fi {E[gi (X))]}, i = 1, . . . , n,
our goal is to determine a suitable quote for our own insurance contract.
Assuming the risk X is parameterized by θ ∈ Rd , and since loading functions fi are unknown, we adopt a
Bayesian learning strategy with a prior distribution p(θ). The procedure is as follows:
1. Sample a parameter value θ∗∗

2. Compute the pure premiums pθi for each insurance policy
3. Fit an isotonic regression f ∗ , to learn the relationship between commercial premia πi = Eθ∗ [gi (X))]∗
and pure premia pθi
4. Build synthetic market data D∗ by applying the estimated loading f ∗ to the pure premium
5. If the observed and synthetic market data are close, store θ∗ and f ∗ .
This iterative process provides a sequence of parameter-loading function pairs, enabling us to price ourown policies. Our solution, inspired by indirect inference methodologies, resembles Approximate Bayesian
Computation (ABC) algorithms, yielding an approximate posterior distribution p(θ|D).
Acknowledgement: Pierre-O’s work is conducted within the Research Chair DIALOG under the aegis of
the Risk Foundation, an initiative by CNP Assurances.

PARALLEL SESSIONS III
Mortality 2
NON-CHRONOLOGICAL AGES AND THE LIFETIME SHIFTING:INVESTIGATING A NEW PARADIGM IN MORTALITY MODELING ANDFORECASTING
A.R. Bacinello1 , R. Maggistro1 , M. Marino1,∗
1 Department of Economics, Business, Mathematics and Statistics “Bruno de Finetti”, University of Trieste

bacinel@units.it, rosario.maggistro@deams.units.it, mario.marino@deams.units.it (∗ corresponding author)
Longer lives are an achievement and the course of longevity is a compelling matter of interest for policymakers, demographers, and actuaries. Various and pioneering studies concerning mortality modeling andforecasting have been introduced in the literature, all of which share an implicit assumption: the age flows
chronologically. However, recent research works highlighted the concept of non-chronological age (see,e.g., [3], [2], [4], [1]), suggesting new insights for mortality modeling and forecasting. Then, the present

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work aims to investigate to what extent the potential non-chronological pace of aging affects the usual mortality and longevity analysis. Since the course of lifespan is increasingly influenced by unobservable risk
factors altering the chronological pace of aging, we exploit the concept of individual frailty (see, e.g., [5]) as
an unobservable random quantity shifting the chronological human lifetime. We first illustrate how technically construct the non-chronological lifetime starting from a chronological Gompertz mortality framework.
Thereafter, we define the mortality intensity under the non-chronological lifetime, discussing the associatedfitting and forecasting methods. In particular, we refer to the Poisson maximum likelihood framework forfitting purposes, while a multivariate random walk with drift is employed to project the mortality intensity
parameters. Finally, we empirically test our methodological framework on the Human Mortality Databasemortality data, for both genders. Our analysis highlights both the goodness of fit and the prediction accuracyof the non-chronological mortality intensity on the observed mortality experience.
Acknowledgement: The authors are grateful to the Society of actuaries, Research Insititute, for its support through the funded project “A biological inspired perspective in longevity risk management: which
implications for actuaries?”, N. KP199.

References[1] Alvarez J-A, Vaupel JW (2023) Mortality as a Function of Survival. Demography 60(1):327–342.
[2] Huang H, Milevsky MA, Salisbury TS (2017) Retirement spending and biological age. Journal of
Economic, Dynamics & Control 84:58–76.
[3] Jackson SHD, Weale MR, Weale RA (2003) Biological age-what is it and can it be measured?.
Archives of Gerontology and Geriatrics 36(2):103–115.
[4] Milevsky MA (2020) Calibrating Gompertz in Reverse: What is your longevity-risk-adjusted global
age?. Insurance: Mathematics and Economics 92:147–161.
[5] Pitacco E (2019) Heterogeneity in mortality: a survey with an actuarial focus. European Actuarial
Journal 9:3–30.

A MODIFIED POISSON INVERSE GAUSSIAN LEE-CARTER MORTALITY
MODEL
Funda Karaman1
1 Department of Actuarial Science, Hacettepe University, Ankara, Türkiye

fundakaraman@hacettepe.edu.tr
Mortality estimation is having great effect on the survival and achievement of many institutions and organizations: planning the social security system, calculating actuarial premiums and reserves for insurancecompanies, funding for organizations that make commitments for retirement, financing health systems, calculating pecuniary damages as a result of death and bodily damages in courts.

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Numerous models have been proposed since Gompertz published his law of mortality in 1825 [1] andseveral mortality forecasting models have been proposed in the last years. Lee and Carter (1992) [2] is
one of the most successful among the extrapolative methods, and has since received a great deal of attention. In commonly used applications, the number of deaths is assumed to have a Poisson distribution[3].
However, it is observed that the mean and variances of the number of deaths are not the same in country applications. Mixed poisson models have been proposed to eliminate this problem: Poisson-Gamma,
Poisson-Lognormal[4].
In this study, Poisson-Inverse gaussian mixed LC mortality model is proposed. EM algorithm is used forparameter estimation. I use data from the Human Mortality Database for, Australia, Italy and France. The
data are divided into the in-sample (fitting) period and out-of-sample (forecasting) period. Data from 1950
to 2010 represent fitting period and 2011 to 2019 forecasting period. The results indicate that heterogeneity
in mortality is important for mortality modeling. According to goodness of fit tests, proposed model gives
better results.

References[1] Tjørve KM, Tjørve E (2017) The use of Gompertz models in growth analyses, and new Gompertzmodel approach: An addition to the Unified-Richards family. PloS one 12(6).
[2] Lee RD, Carter LR (1992) Modeling and forecasting US mortality. Journal of the American statisticalassociation 87(419):659–671.
[3] Brouhns N, Denuit M, Van Keilegom I (2005) Bootstrapping the Poisson logbilinear model for mortality forecasting. Scandinavian Actuarial Journal 2005(3):212–224.
[4] Wong JS, Forster JJ, Smith PW (2019) Bayesian mortality forecasting with overdispersion.

BAYESIAN MODELLING FOR CANCER MORTALITY – INEQUALITIES,COVID-19 IMPACT AND FUTURE PROJECTIONS
Ayşe Arık1 , Andrew Cairns1 , George Streftaris1,∗
1 Department of Actuarial Mathematics and Statistics, Heriot-Watt University, and the Maxwell Institute forMathematical Sciences, UKa.arik@hw.ac.uk, a.j.g.cairns@hw.ac.uk, g.streftaris@hw.ac.uk (∗ corresponding author)
Modelling cancer risk trends and differences is important for insurance purposes and can impact pricing
and reserving in health insurance areas such as critical illness insurance and care provision. In this work
[1] we investigate mortality rates for two major cancer types, breast cancer and lung cancer, using general
population data in England. Patterns in cause-specific cancer mortality rates are modelled under a Bayesianhierarchical setting, and rates are investigated by age, gender, regions of England, income deprivation, average age-at-diagnosis and non-smoker prevalence. Rates are then projected into future years using Bayesian
forecasting, through a time series random-walk with drift for period-related effects. Motivated by health57

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disruptions caused by the Covid-19 pandemic, this also allows us to investigate the potential impact of diagnosis delays on future cancer mortality. We estimate future excess type-specific cancer deaths, based on
scenarios involving an increase in average age-at-diagnosis. The analysis reveals considerable socioeconomic inequalities in lung cancer mortality, which persist over time and into the future. Our research also
found that delays in cancer diagnosis, can result in significant excess in lung cancer mortality, that additionally differs by age, region and deprivation. At the same time, marginally significant regional differences areindicated for breast cancer mortality in future years.

References[1] Arık A, Cairns AJG, Streftaris G (2024) Cancer mortality projection: disparities, COVID-19, and latediagnosis impact. arXiv:2405.05643.

A NOVEL FRAMEWORK OF STOCHASTIC MORTALITY MODELLINGPeter Hatzopoulos1,∗ , Apostolos Bozikas1
1 University of Piraeus

xatzopoulos@unipi.gr (∗ corresponding author)
Stochastic mortality models include age - period - cohort components that must be appropriately estimatedto produce efficient mortality forecasts. This work proposes an estimation methodology that is based on thefollowing procedure. First, we incorporate appropriate generalized linear models (GLMs) to obtain smoothmortality estimates, and then we apply sparse principal component analysis to extract the related age – period- cohort components. We identify the optimal number of the incorporated age, period and cohort effects ofa mortality model by the unexplained variance ratio (UVR) metric to maximize the captured variance of themortality data, and to regulate the sparsity of the model with the aim of acquiring distinct and significant
stochastic components. Our methodology is applied to various mortality datasets.
Acknowledgement: This work has been partly supported by the University of Piraeus Research Center.

References[1] Hatzopoulos P, Haberman S (2011) A dynamic parameterization modelling for the age-period-cohort
mortality. Insurance: Mathematics and Economics 49(2):155–174.
[2] Hatzopoulos P, Sagianou A (2020) Introducing and Evaluating a New Multiple-Component Stochastic
Mortality Model. North American Actuarial Journal 24(3):393–445.
[3] Lansangan JR, Barrios EB (2009) Principal Components Analysis of Nonstationary Time Series Data.
Statistics and Computing 19(2):173–187.
[4] Luss R, Aspremont A (2006) DSPCA: a Toolbox for Sparse Principal Component Analysis.

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Statistical Methods 1
HETEROGENEOUS EXTREMES IN THE PRESENCE OF RANDOMCOVARIATES AND CENSORING
Christoffer Øhlenschlæger1,∗ , Martin Bladt1
1 Department of Mathematical Sciences, University of Copenhagen, Denmark

choh@math.ku.dk (∗ corresponding author), martinbladt@math.ku.dk
There are several applications where data containing extreme values and censoring come into play. For
instance, observations of survival times in medical studies are naturally right-censored and cured patients
may live much longer than the average. Sometimes the latter effect can be so severe that the lifetime
distributions of the cohort may adequately be modeled by a heavy-tailed distribution. Other examples arise
when analysing catastrophic events, e.g. insurance claim sizes in certain lines of business may be verylarge and paid out throughout several years, incurring in incomplete information. A common feature ofthese type of studies is the presence of covariates, which are commonly the center of interest when drawing
conclusions, for instance to quantify treatment effect differences on subpopulations, or determining risk
classes within an insurance portfolio.
This paper is devoted to building the mathematical foundations for statistical inference of data exhibiting
heavy-tails, censoring and covariates. To handle this problem, we employ an idea from [4], which analyses
estimators derived as integrals with respect to the product-limit estimator (cf. [3]) at normalized upper order
statistics; however, we simultaneously incorporate the idea of [6], where the inclusion of random covariatesin handled elegantly in a censoring context. The extension is relevant on two fronts. First, the incorporationof covariates greatly widens the practical relevance of models for heavy-tailed and right-censored data, enabling the use of a larger and more versatile group of estimators. Secondly, from a mathematical perspective
there are several hurdles to overcome, which necessitates the formulation of appropriate and lax conditions
on the distribution of the data and estimators which allows for tractable asymptotic behaviour. These conditions, in turn, lead to interesting features that are not present in the non-extreme counterparts in [6]. For
instance, the covariate distribution changes support in the limit, concentrating on covariates giving rise to
the most catastrophic events, and the original distribution is re-weighted according to the regularly-varying
components of the conditional distributions. In applications, these features can be used asses not only how
extreme events occur, but also which covariates are the drivers of such events.
This paper extends the results from [4] in the Fréchet max-domain of attraction and includes covariates. The main result is likewise a decomposition of extreme Kaplan–Meier integrals into exchangeable
sums, and we establish that the remainder term again vanishes. However conceptually simple, the inclusionof covariates requires extending some fundamental results and bounds of univariate extreme value theory.
Among others, we highlight the extension of the well-known Karamata representation and Potter’s bounds
to a uniform context. Furthermore, we provide suitable uniform-type conditions under which we may establish that the dependence of the exchangeable sums disappears in the limit, allowing us to show consistency
and three central limit theorems. As a by-product, we study the distribution of the covariates that lead to tailevents, which is of importance for the limiting distribution in the CLT, but is also an interesting result on its
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own. Apart from technicalities, the general structure of the proofs follows [4, 1, 6, 2], with general facts andnotation from extreme value theory following [5].

References[1] Stute W (1995) The Central Limit Theorem Under Random Censorship. The Annals of Statistics
23(2):422–439.
[2] Segers J (2001) Residual estimators. Journal of Statistical Planning and Inference 98(1):15–27.
[3] Kaplan EL, Meier P (1958) Nonparametric Estimation from Incomplete Observations. Journal of theAmerican statistical association 53(282):457–481.
[4] Bladt M, Rodionov I (2024) Censoredhttps://doi.org/10.48550/arXiv.2312.10499.

extremevalue

estimation.

Preprint,[5] De Haan L, Ferreira A (2006) Extreme Value Theory: An Introduction, Vol. 3. Springer.
[6] Stute W (1996) Distributional Convergence under Random Censorship When Covariables Are Present.
Scandinavian Journal of Statistics 23(4):461–471.

MODELING LOWER-TRUNCATED AND RIGHT-CENSORED INSURANCE
CLAIMS WITH AN EXTENSION OF THE MBBEFD CLASS
Selim Gatti1,∗ , Mario Wüthrich1
1 RiskLab, Department of Mathematics, ETH Zurichselim.gatti@math.ethz.ch (∗ corresponding author), mario.wuehtrich@math.ethz.ch
Insurance contracts in general insurance often involve deductibles and maximal covers. Denote by X thetotal financial loss faced by an insured. The insurance claim Y after subtracting the deductible d > 0 andwith a maximal cover of size M > 0 is given by
Y = min {(X − d)+ , M } | X > d.
We say, this financial loss is lower-truncated at d > 0 and right-censored at M > 0 (after subtracting
the deductible). Statistical modeling of lower-truncated and right-censored claims is a notoriously difficult
problem since most statistical models have an unbounded support, e.g., the supports of the gamma andthe log-normal distributions are the entire positive real line R+ . In many cases, this implies that fitting
a statistical model to lower-truncated and right-censored data is not a problem that is easily analyticallytractable. We give an example. Assume the total financial loss X to be an absolutely continuous randomvariable on (0, ∞). In this case, the log-likelihood function of the lower-truncated and right-censored claims
Y ∈ (0, M ] for an unknown parameter θ is given by
1 − Fθ (d + M )fθ (d + Y )θ 7→ ℓY (θ) = log
1{Y <M } + log
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where Fθ and fθ denote the distribution and the density of the total financial loss X, respectively. Fitting such a model with MLE can be difficult because we need an analytically tractable form for both thedensity fθ (·) and its distribution function Fθ (·). In such cases, one either needs to rely on numerical integration of the density (which can be computationally demanding) or one uses a version of the ExpectationMaximization (EM) algorithm by interpreting the lower-truncation and right-censoring as a missing information problem; we refer to Verbelen et al. [4], Fung et al. [2] and Sections 6.4.2 and 6.4.3 in Wüthrich–Merz[5]. However, also this EM algorithm approach has its drawbacks as it requires tractability of conditional
tail expectations and reasonable dispersion estimates in multi-dimensional parameter settings.
We take a different approach in our paper [3] to solve the fitting problem of lower-truncated and rightcensored data. In the reinsurance literature, Bernegger [1] introduced so-called MBBEFD exposure curves
for exposure rating. These exposure curves are based on the assumption that there is a maximal cover M , andthey directly describe right-censored claims up to this maximal cover. Differentiating twice these MBBEFD
exposure curves provides us with densities being absolutely continuous on the interval (0, M ) and having apoint mass in M . We extend this class of MBBEFD distributions to a bigger class of models that we callthe Bernegger class. This new class of distributions allows to model lower-truncated and right-censoredrandom variables with fully tractable distributions, densities, point masses and means, i.e. they are all ofclosed form.
Our contribution is to show that the Bernegger class is a rich family of distributions including monotonically decreasing densities, unimodal densities and monotonically increasing densities, and our extension
provides new families of lower-truncated and right-censored random variables that allow for skewness inthe absolutely continuous part of the distribution. This is of particular interest because unimodal skewed
densities are suited for modeling lower-truncated and right-censored claims in general insurance. By fittinga real dataset consisting of private property insurance claims, we introduce a couple of explicit models belonging to the Bernegger class that allow for unimodal and skewed densities. In particular, the distributionsof lower-truncated and right-censored exponential and logistic random variables belong to the Berneggerclass.
Finally, we consider the situation where the insurer is interested in understanding how a change in the
deductible or the maximal cover affects the expected claim size. For this, we first emphasize that, typically,
the insurer only observes the lower-truncated and right-censored claim Y . That is, for statistical modeling,neither are the claims below the deductible d known, nor are the exact claim sizes above the maximal cover
M known. In general, this does not allow us to obtain a unique extrapolation below the lower-truncation
point and above the right-censoring point since there are infinitely many candidates. Therefore, we can only
perform the opposite operation of either increasing the deductible or decreasing the maximal cover, and weshow that the Bernegger class is closed under these transformations.

References[1] Bernegger S (1997) The Swiss Re exposure curves and the MBBEFD distribution class. ASTIN Bulletin 27(2):99–111.
[2] Fung TC, Badescu AL, Lin XS (2022) Fitting censored and truncated regression data using the mixtureof experts models. North American Actuarial Journal 26(4):496–520.

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[3] Gatti S, Wüthrich MV (2023) Modeling lower-truncated and right-censored insurance claims with anextension of the MBBEFD class. arXiv:2310.11471.
[4] Verbelen, R., Gong, L., Antonio, K., Badescu, A., Lin, S. Verbelen R, Gong L, Antonio K, Badescu
A, Lin S (2015) Fitting mixtures of Erlangs to censored and truncated data using the EM algorithm.
ASTIN Bulletin 45(3)729–758.
[5] Wüthrich MV, Merz M (2023) Statistical Foundations of Actuarial Learning and its Applications.
Springer Actuarial.

ISOTONIC REGRESSION FOR VARIANCE ESTIMATION AND ITS ROLE
IN MEAN ESTIMATION AND MODEL VALIDATION
Łukasz Delong1,∗ , Mario Wüthrich2
1 University of Warsaw, Faculty of Economic Sciences
2 ETH Zürich, Department of Mathematics

l.delong@uw.edu.pl (∗ corresponding author), mario.wuethrich@math.ethz.ch
We study isotonic regression which is a non-parametric rank-preserving regression technique. Under the assumption that the variance function of a response is monotone in its mean functional, we investigate a novel
application of isotonic regression as an estimator of this variance function. Our proposal of variance estimation with isotonic regression is used in multiple classical regression problems focused on mean estimationand model validation. In a series of numerical examples, we (1) explore the power variance parameter ofthe variance function within Tweedie’s family of distributions, (2) derive a semi-parametric bootstrap underheteroskedasticity, (3) provide a test for auto-calibration, (4) explore a quasi-likelihood approach to benefit
from best-asymptotic estimation, (5) deal with several difficulties under lognormal assumptions. In all these
problems we verify that the variance estimation with isotonic regression is essential for proper mean estimation and beneficial compared to traditional statistical techniques based on local polynomial smoothers.

AALEN–JOHANSEN: REFRESHED AND REFINED
Christian Furrer1
1 University of Copenhagen, Department of Mathematical Sciences

In multi-state Markov models and subject to for instance right-censoring, the Aalen–Johansen estimator allows for non-parametric estimation of transition probabilities. This remains the case in non-Markov models
if so-called landmarking, which is a subsampling technique, is employed. Given that the Markov assumption
rarely is satisfied in practice, the landmark Aalen–Johansen estimator is a nice addition to the actuarial toolbox. In this talk, I introduce the estimator and discuss two recent theoretical contributions in the non-Markov
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regime that increase and improve its applicability in life insurance.
The first contribution relates to valuation and is an extension of the estimator that allows for weights.
Certain weights need to be considered for the estimation of so-called scaled payments, which arise from theinclusion of incidental policyholder options such as free-policy conversion or stochastic retirement. (Basedon joint work with Theis Bathke from the Carl von Ossietzky University of Oldenburg.)
The second contribution relates to risk management and is the validation of the bootstrap for the Aalen–
Johansen estimator in the non-Markov regime. This allows for the construction of, for instance, confidencebounds for estimates of the prospective reserve. (Based on joint work with Martin Bladt from the Universityof Copenhagen.)

Mathematical Finance 1
CONVEX HEDGERS AND FAIR CONVEX COST-OF-CAPITALVALUATIONS IN A SINGLE PERIOD FRAMEWORKJan Dhaene1 , Alexander Kukush2 , Daniel Linders3 , Atibhav Chaudhry1,4
1 KU Leuven, Leuven, Belgium
2 National Taras Shevchenko University, Kyiv, Ukraine
3 University of Amsterdam, Amsterdam, Netherlands
4 University of Melbourne, Melbourne, Australia

Jan.Dhaene@kuleuven.be, Alexander Kukush@univ.kiev.ua, D.H.Linders@uva.nl,
Atibhav.Chaudhry@kuleuven.be
In this paper, we build a general framework for hedging and valuating hybrid insurance claims. Our contribution is twofold. First, we generalise hedgers proposed by Dhaene et al. [1] and Barigou et al. [2] toallow for all non-strictly convex objective functions. The wider range of objective functions allows the user
to penalise gains and losses separately. The hedgers resulting from non-strictly convex objective functions
have a wide variety of properties and underlying actuarial valuations. Second, our work introduces costof-capital valuations, which use the non-strictly convex objective function to value the residual risk arisingfrom the hedge. Cost-of-capital valuations generalise the valuation principles proposed by Dhaene et al. [1]and Barigou et al. [2], resulting in a unified framework for fair valuations.
In our work, we adopt the two-step valuation approach proposed by Dhaene et al. [1] for the valuationof hybrid insurance liabilities. In a first step, the information in the financial market is used to set up a hedge
which replicates the payout of the hybrid product ‘as close as possible’ using a an objective function. In asecond step, we adopt the principles proposed by Barigou et al. [2] to use another hedge to set up a riskmargin for the residual risk. Combining these two approaches allows us to define cost-of-capital valuations.
Cost-of-capital valuations equal the cost of the hedging strategy in the first step plus the cost of capital of
the hedging strategy in the second step.
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which can be constructed using a hedge with non-strictly convex objective functions. We further show thatthe class of convex cost-of-capital valuations is equivalent to the class of hedge-based valuations introduced
by Dhaene et al. [1], and two-step valuations introduced by Pelsser & Stadje [3].
Acknowledgements: Jan Dhaene gratefully acknowledges funding from FWO and F.R.S.-FNRS under the
Excellence of Science (EOS) programme, project ASTeRISK (40007517). Daniel Linders and Jan Dhaeneacknowledge the financial support of the KU Leuven Research Council (BOF) under grant C14/21/089.
Atibhav Chaudhry acknowledges the financial support from the Australian Government Research Training Program (RTP) Scholarship, a Faculty of Business and Economics Doctoral Program Scholarship, aUniversity of Melbourne Research Scholarship and the 2021 Kilmany Scholarship.

References[1] Dhaene J, Stassen B, Barigou K, Linders D, Chen Z (2017) Fair valuation of insurance liabilities:
Merging actuarial judgement and market-consistency. Insurance: Mathematics and Economics 76:14–
27.
[2] Barigou K, Bignozzi V, Tsanakas A (2022) Insurance valuation: A two-step generalised regression
approach. ASTIN Bulletin: The Journal of the IAA 52(1):211–24.
[3] Pelsser A, Stadje M (2014) Time-consistent and market-consistent evaluations. Mathematical Finance:
An International Journal of Mathematics, Statistics and Financial Economics 24(1):25–65.

EFFICIENT HEDGING OF LIFE INSURANCE PORTFOLIO FOR
LOSS-AVERSE INSURERS
Edouard Motte1,∗ , Donatien Hainaut1
1 LIDAM-ISBA, Université Catholique de Louvain, Belgium

edouard.motte@uclouvain.be (∗ corresponding author), donatien.hainaut@uclouvain.beThis paper investigates the hedging of equity-linked life insurance portfolio for loss-averse insurers. We
consider a general arbitrage-free financial market and an actuarial market composed of n-independent policyholders. As the combined market is incomplete, perfect hedging of any actuarial-financial payoff is notpossible. Instead, we study the efficient hedging of n-size equity-linked life insurance portfolio for insurers
who are only concerned with their losses. To this end, we consider stochastic control problems (under the
real-world measure) in order to determine the optimal hedging strategies that either maximize the probability of successful hedge (called quantile hedging) or minimize the expectation for a class of shortfall loss
functions (called shortfall hedging). We show that the optimal strategies depend both on actuarial and financial risks. Moreover, these strategies adapt not only to the size of the insurance portfolio but also to therisk-aversion of the insurer. Under the additional assumption of complete financial market, we derive theexplicit forms of the optimal hedging strategies. The numerical results show that, for loss-averse insurers,

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the optimal strategies outperform the optimal mean-variance hedging strategy, demonstrating the relevanceof adopting the optimal strategy according to the insurers’ risk aversion and portfolio size.
Acknowledgement: Edouard Motte was financially supported by the Fonds de la Recherche Scientifique FNRS through a FRIA grant.

THE THREE-STEP METHOD IN A DYNAMIC SETTING
Oussama Belhouari1,∗ , Daniel Linders2 , Pierre Devolder1
1 Catholic University of Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences, Voie duRoman Pays 20, 1348 Louvain-La-Neuve, Belgium
2 University of Amsterdam, Faculty of Economics and Business, Section Quantitative Economics,

Roetersstraat 11, 1001 NJ Amsterdam, Netherlands
oussama.belhouari@uclouvain.be (∗ corresponding author), d.h.linders@uva.nl,
pierre.devolder@uclouvain.be
A crucial issue in a dynamic framework, is how risk valuations at different times are interrelated. In this regard, the notion of time consistency was widely introduced and discussed in the literature. A time-consistent
dynamic valuation is a pricing method according to which a product that will be, in almost all states of nature, cheaper than another one at a future date should already be cheaper today. Common actuarial premium
principles are not time consistent. To this end, we link the latter with an iterated property. This paper
aims at constructing a market-consistent, time-consistent, dynamic version of the Three-step method as
introduced in [1], employing a backward iteration scheme. The backward scheme is exemplified in a dualiteration approach using a classical application, specifically a Pure Endowment. Furthermore, we explore
the continuous-time limit of the Three-step method, incorporating profit-sharing into the Pure Endowment
to investigate a hybrid life payoff. Our analysis reveals that, due to time consistency, prices undergo a substantial increase. To address this, and in accordance with [2], we present a time-consistent variant of theThree-step method that integrates a single security margin throughout the entire backward iteration process.
Keywords: Premium principles · time-consistent · fair dynamic valuation · backward iteration scheme ·hybrid life payoff

References[1] Deelstra G, Devolder P, Gnameho K, Hieber P (2020) Valuation of hybrid financial and actuarial
products in life insurance by a novel three-step method. ASTIN Bulletin: The Journal of the IAA
50(3):709–742.
[2] Devolder P, Lebègue A (2016) Compositions of conditional risk measures and solvency capital. Risks,
4(4):49.

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OPTIMAL REINSURANCE MAXIMISING DIVIDENDS: AN
INFINITE-DIMENSIONAL APPROACH AND NUMERICAL RESULTS∗

Debora Daniela Escobar1 , Hirbod Assa2 , Yunzhou Chen3
1 Department of Actuarial Mathematics and Statistics, Heriot-Watt University
2 School of Mathematics, Statistics and Actuarial Science, University of Essex
3 Department of Mathematical Sciences, University of Liverpool

d.escobar@hw.ac.uk (∗ corresponding author), h.assa@essex.ac.uk, natalie.lothar@gmail.com
We study the optimal reinsurance problem in a discrete-time dynamic framework that maximizes the lifetime
dividends (LD) of an insurance company. We formulate this problem as an infinite-dimensional problem andsolve three problems. a) We maximise the LD only under the budget constraint (surplus dynamics) b) we
incorporate a solvency condition for the insurer. Both settings prove to be equivalent to solving static optimal
reinsurance problems and in both cases the optimal policy is a layered policy. From the setting a) we do
not gain more information than the optimal reinsurance policy, while the constraint added in b) gives the
optimal surplus and dividends that maximise the LD. A positive result is that the optimal dividends are afunction of the surplus, as dividend rules are commonly given, although the optimal surplus lacks dynamics.
Our results suggest to solve a third problem. In this last setting c) dividends are no longer free parameters,
but a given pre-defined dividend rule. For c) we require techniques of infinite-dimensional problems. We
obtain optimal multi-layered policies as well, although the solutions are more complex as they dependon Lagrangian multipliers that are unknown. Solving c) for the well-known barrier dividend simplifies
the optimization problem and motivates a numerical approach to estimate the multi-layered policies of c).
All optimal policies depend on the distortion risk measure that defines the reinsurance premium. Whilefor a)-b), the layers of the optimal policies depend on how many times the distortion measure crosses a
region, our numerical solutions show that the layers of the optimal policies for c) also depend on the risk
aversion given by the distortion measure. We present the differences between the three settings when thereinsurance premium is given by the Value-at-Risk (VaR), Average Value-at-Risk (AVaR) and Glue Valueat-Risk (GlueVaR), and observe their impact in the distribution of the surplus an dividends. This study
not only provides theoretical insights into the optimal reinsurance contract design but also offers a practicallinear programming algorithm to approximate policies.

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Nonlife Insurance Mathematics 2
OPTIMAL DIVIDEND FOR AN ORNSTEIN UHLENBECK SURPLUS
Fabio Colpo1,∗ , Julia Eisenberg1
1 TU Wien

fabio.colpo@tuwien.ac.at (∗ corresponding author), julia.eisenberg@tuwien.ac.at
We consider an insurance company whose surplus follows an Ornstein-Uhlenbeck(OU) process driven bya standard Brownian motion. The company pays dividends to its shareholders and seeks to maximise theexpected value of the future discounted dividends. Late dividend payments are penalised not only throughthe usual discounting, but through an additional exponential factor.
We find the optimal strategy for the case of mean-reverting and non-mean-reverting OU processes andillustrate out findings by a numerical example.

ON THE MINIMIZATION OF THE RUIN PROBABILITIES OF TWO
INSURERS IN A RISK-SHARING SCENARIO
E. Fino1,∗ , M. Guerra1,2 , A. Moura1,2
1 CEMAPRE - Mathematics Applied to Forecasting and Economic Decision & REM - Research in

Economics and Mathematics
2 Lisbon School of Economics and Management, University of Lisbon

elisabetefino@iseg.ulisboa.pt (∗ corresponding author), mguerra@iseg.ulisboa.pt, amoura@iseg.ulisboa.pt
We consider an optimal risk-sharing problem in a market with two participants. The two firms have conflicting interests, in the sense that they both seek to absorb the highest proportion of the insurance premium
possible, while also taking on the least amount of risk they can. Furthermore, we introduce a dependency between these two firms, where one of them reaches bankruptcy with probability one if the other one collapses
but the reverse is not verified. We analyse a proportional risk-sharing treaty and a game where both parties
aim to minimize their ruin probabilities. A set of integro-differential equations describing their ruin probability behaviour is derived, and some numerical illustrations provided. Based on those equations, Pareto
equilibrium conditions are obtained.
Acknowledgement: The authors acknowledge financial support from FCT–Fundação para a Ciência e Tecnologia (Portugal), national funding, through research grants EXPL/EGE-ECO/0886/2021 and
UIDB/05069/2020.

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ENHANCING SME FACTORING: A STACKELBERG GAME-BASEDHYBRID PRICING MODEL
Constantin Siggelkow1,∗ , Matthias Scherer1
1 Chair of Mathematical Finance, Technical University of Munich, Parkring 11/II, Garching b. München,

85748, Germany
constantin.siggelkow@tum.de (∗ corresponding author), scherer@tum.de
In supply chain management and trade-credit, buyers of goods or services are often granted a delayed payment goal, and the sellers of the respective goods or services are thus exposed to credit risk. Factoring isa financing decision by which sellers can eliminate that risk from their balance sheet. This service is typically offered on a whole turnover basis, however, SMEs prefer financing on a single debt level, and, hence,
adverse selection emerges as an additional source of risk. This working paper consists of three main chapters, namely the development of a multivariate default model, an optimization problem for the seller and thederivation of a hybrid linear pricing model that covers both default and adverse selection risk. First, as thetrade-credit period we consider is typically not longer than 90 days, we assume a tractable one-parametricmodel for the univariate default times: the exponential distribution. Hence, we let (Ω, F, P) be a probability
space supporting d ∈ N random variables τk , k ∈ {1, . . . , d}, which we define by means of their survival
function
P (τk > t) = e−Λk t , ∀k ∈ {1, . . . , d}, Λk > 0.
Extending the exponential law from the perspective of its lack-of-memory property to a multivariate analogon leads to the Marshall–Olkin distribution, first derived in [1]. Overcoming the implied complexity of theparameters, researchers have developed and derived a connection between the (extendible) Marshall–Olkin
distribution and the notion of Lévy subordinators. Using this connection, we let the portfolio-default model
consist of n ∈ N>0 risk factors with mn ∈ N>0 categories, respectively. This way, we can define thedefault time for each company k ∈ {1, . . . , d} as the first-passage time of a Lévy subordinator across a unit
exponential threshold:(k)τk = inf{t > 0 : Lt

> εk }.

After setting up the portfolio default model, which allows us to efficiently simulate the set of companies
defaulting in [0, t], we set up a portfolio optimization problem for the seller. This approach is part ofthe class of bi-level optimization problems ([2]) as we are trying to find a price model for the factoring
company by optimizing their opponents decision. After defining the objective function, we state and solve
the following optimization problem:
min gα∗ (x)
x

s.t.

d
X

x k Mk ≤ P ∗k=1

x ∈ [0, 1]d .
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We show strong convexity of this function and argue why it is necessary to use a stochastic gradient descentalgorithm to solve this problem. We conclude with almost sure convergence of the underlying algorithmand derive conditions for both seller and factoring company to enter into an agreement, namely covering
expected losses and paying less than what is potentially earned. This implies certain boundaries for the
price, i.e. a price interval. Next, we assume, that in case of a default, a factoring company’s recovery value
is higher than the one from the seller (follows as the seller is assumed to be a SME). Then, we show that theprice interval given by
h

i

fk := E 1 − κfk ac 1{k∈St } 1 + ψ ,for debtor k ∈ {1, . . . , d} satisfies the before derived interval conditions and enables the possibility toinclude a dynamic part in the price. κfk ac represents the recovery value of the factoring company, St the setof defaulted companies in [0, t] and ψ = c + m + φ is a combination of management costs, margin and the
dynamic part φ. Lastly, we embed the simplest data-rich modeling approach for φ in our analysis, namely
a linear dynamic pricing model with demand covariates [3]. In summary, we derive a lower and an upperbound for the price and then show that it suffices to deploy a linear model as a mix of a static and a dynamic
part to cover both default and adverse selection risk. This way, factoring companies can offer coverage
on a single debt level without underestimating the risk. Munich Re, the largest reinsurer in the world hassponsored this project which resembles the interest of the industry in this field.

References[1] Marshall A, Olkin I (1967) A multivariate exponential distribution. Journal of the American Statistical
Association 62:30–44.
[2] Burtscheidt J, Claus M (2020) Bilevel linear optimization under uncertainty. Springer optimization andits applications 161:485–511.
[3] Qiang S, Bayati M (2016) Dynamic pricing with demand covariates. SSRN Electronic Journal.

CURE MODELS: FROM MIXTURE TO MATRIX DISTRIBUTIONSMartin Bladt1 , Jorge Yslas2,∗
1 University of Copenhagen
2 University of Liverpool

martinbladt@math.ku.dk, Jorge.Yslas-Altamirano@liverpool.ac.uk (∗ corresponding author)
Survival analysis has received significant attention in recent decades, particularly in estimating the cure rate
- the proportion of subjects who will never experience an event. Mixtures have been the established parametric model for estimating the cure rate and associated survival curves. In this talk, we introduce a novel
cure model based on phase-type distributions, which are a generalization of mixtures and rely on a Markovian latent path. The proposed model incorporates a hidden Markov jump process, enabling a proportion of69

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subjects to be immune at inception and another proportion to become immune at later time points, resulting in an overall cure rate. In addition, we present a unified approach to regression on both the cure rate
and the distribution of susceptibles. The added parameters provide the model with enhanced flexibility andinterpretability compared with traditional cure models. Expectation-maximization algorithms are derived
to estimate all models, which are then exemplified with synthetic and real-life data. For insurance applications, this approach allows insurers to assess risk and calculate premiums more accurately, for instance, bydifferentiating between those likely to recover and those with chronic conditions in health insurance. Other
applications include lapse or credit risk modeling.

TUESDAY, SEPTEMBER 10th
PLENARY SESSION II
REVERSE MORTGAGES: IMPACT ON HOUSEHOLD FINANCIALSUSTAINABILITY
Merce Claramunt1
1 Universitat de Barcelona

mmclaramunt@ub.edu
Reverse mortgage is one of the products (perhaps the main one) that is good to obtain additional income
by using the habitual residence as collateral. This paper analyzes the effects that contracting a reverse
mortgage has on the finances of families of a country or group whose members who aged 65 or older are
the sole owners of the 100% of the property, regardless of the receipt of a retirement pension. For thispurpose, an economic-financial model based on the life cycle model is defined, which considers a double
source of randomness: mortality and dependence of family members. Long-term effects are measured using
probabilistic, temporal and monetary indicators. For each country, the model must be adapted according to
the legal framework for retirement and long-term care benefits and for the actuarial mortality and long-termcare tables. We also studied the importance of the socioeconomic group to which the family belongs inquantifying these effects. As an illustration, this model was applied on Spanish families using data fromthe Spanish Survey of Household Finances 2017. The results obtained indicate that a family in Spain thatmeets the conditions for contracting a reverse mortgage sees, on average, an increase in its initial income
and a decrease in both its probability of having liquidity problems in the future and the value of this lackof liquidity. It is also concluded that family composition influences the magnitude of these positive effects.
We also conclude that the effects are very different depending on the group: regarding only the effects ofhiring a reverse mortgage on the income of the family, widowed women aged between 81 and 85 years,
with low income and expenses as well as little net wealth, and a habitual residence that represents half ofher net wealth (Cluster 1) are the most benefited; considering that the highest impact indicators are on the70European Actuarial Journal Conference 2024
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probability of illiquidity and on the value of lack of liquidity, the use of reverse mortgages benefits more
the families in Cluster 3 (high income and expenses and really high net wealth, head of household aged
between 76 and 80 years) and less the families in Cluster 2 (medium income, net wealth and expenses, headof household aged between 65 and 75 years).

PARALLEL SESSIONS IV
Climate Risks 2
INTERGENERATIONAL-DICE MODEL: AN INTEGRATED ASSESSMENTANALYSIS ON THE EFFECTS OF CLIMATE CHANGE ON SOCIALSECURITY SYSTEMS
Ivan Fonseca Diaz1,∗ , Séverine Arnold1
1 University of Lausanneivanalexis.fonsecadiaz@unil.ch (∗ corresponding author), severine.arnold@unil.ch
Integrated Assessment Models (IAMs) are widely used approaches in climate change analysis due to theirunique ability to represent multiple natural and social systems in a unified framework. These models havebeen primarily used for depicting hypothetical socioeconomic pathways[5, 6, 7], evaluating mitigation policies, and estimating the uncertainties of different plausible scenarios of climate change[3]. One of thepioneering IAMs in the analysis of the economic impacts of climate change is the Dynamic Integrated
Climate-Economy (DICE) model. First introduced by Nordhaus [1, 4], this model is based on a neoclassical economic growth theory, which determines optimal future consumption through investments in capital,
education, and technology. Additionally, this model incorporates the ”natural capital” of the climate system
as a capital stock, thus incentivizing carbon emission reductions while optimizing future consumption.
Despite representing social and natural systems with relative rigor, the DICE model and other IAMs
neglect to consider the intricate dynamics of consumption and savings across multiple coexisting generations, a crucial aspect to consider if one aims to analyse the impact of climate changes on social security
systems. This shortcut may be due to the primary methodological requirement of IAMs, which calls for simplicity and transparency in their representations. To address this issue, we extend the DICE model to allow
for intergenerational consumption and saving allocations in a simple yet comprehensive way. Additionally, we introduce a consistent model representation of a social security system for retirement benefits. Ourinnovative approach to modeling consumption and savings dynamics of different generations not only provides a new perspective on the economic cost of carbon emissions by including its impacts on social security
systems, but also offers a practical tool for depicting plausible global trajectories of carbon emissions and atmospheric temperatures. Moreover, it presents an alternative framework for analyzing the intergenerational
equity of climate change and mitigation policies, thereby contributing to the ongoing policy discussions in71

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this area.

References[1] Nordhaus WD (1992) The ‘DICE’model: background and structure of a dynamic integrated climateeconomy model of the economics of global warming.
[2] Nordhaus WD (2011) Estimates of the social cost of carbon: background and results from the RICE2011 model. National Bureau of Economic Research.
[3] Nordhaus W (2017) Integrated assessment models of climate change. NBER Reporter 3:16–20.
[4] Nordhaus W (2018) Evolution of modeling of the economics of global warming: changes in the DICE
model, 1992–2017. Climatic change 148(4):623–640.
[5] O’Neill BC, Kriegler E, Riahi K, Ebi KL, Hallegatte S, Carter TR, Mathur R, Van Vuuren DP (2014) A
new scenario framework for climate change research: the concept of shared socioeconomic pathways.
Climatic change 122:387–400.
[6] O’Neill BC, Kriegler E, Ebi KL, Kemp-Benedict E, Riahi K, Rothman DS, Van Ruijven BJ, Van
Vuuren DP, Birkmann J, Kok K, et al. (2017) The roads ahead: Narratives for shared socioeconomic
pathways describing world futures in the 21st century. Global environmental change 42:169–180.
[7] Riahi K, Van Vuuren DP, Kriegler E, Edmonds J, O’neill BC, Fujimori S, Bauer N, Calvin K, Dellink R,
Fricko O, et al. (2017) The Shared Socioeconomic Pathways and their energy, land use, and greenhousegas emissions implications: An overview. Global environmental change 42:153–168.

OPTIMAL DIVIDEND STRATEGIES FOR A CATASTROPHE INSURER
WITH IRREVERSIBLE CLIMATE CHANGE
Nora Muler1,∗ , Hansjoerg Albrecher2 , Pablo Azcue1
1 Department of Mathematics and Statistics, Universidad Torcuato Di Tella, Buenos Aires
2 Faculty of Business and Economics , University of Lausanne

nmuler@utdt.edu (∗ corresponding author), hansjoerg.albrecher@unil.ch, pazcue@utdt.edu
In this talk we present the problem of optimally paying out dividends from an insurance portfolio, when
the criterion is to maximize the expected discounted dividends over the lifetime of the company and theportfolio contains claims due to natural catastrophes, modelled by a shot-noise Cox claim number process.
Furthermore, we include an stochastic irreversible climate change that increases the intensity of catastrophes
and/or claim sizes. In order to solve this problem, we consider first the case after the irreversible climatechange, and then using this solution as a known function, we solve the problem before the irreversible
climate change happens (taking into account that at an stochastic time the climate change will occur). In
each step, the optimal value function is a solution of a two-dimensional stochastic control problem that isshown to be the smallest viscosity of a corresponding Hamilton-Jacobi-Bellman equation, and we see that it72

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can be uniformly approximated through a discretization of the space of the free surplus of the portfolio andthe current claim intensity level. We implement the resulting numerical scheme to identify optimal dividend
strategies in each step for such a natural catastrophe insurer, leading to action and non-action regions for thedividend payments as a function of the current surplus and intensity level. This work is a continuation of[1].

References[1] Albrecher H, Azcue P, Muler N (2023) Optimal dividend strategies for a catastrophe insurer. Submitted.
arXiv:2311.05781v1

ON THE DEFINITION OF AN ACTUARIAL CLIMATE INDEX FOR THE
IBERIAN PENINSULA
Nan Zhou1 , José L. Vilar-Zanón1,∗ , José Garrido 2 , Antonio J. Heras Martı́nez1
1 Dept. of Financial and Actuarial Economics & Statistics. Complutense University of Madrid, Spain
2 Dept. of Mathematics and Statistics. Concordia University, Montreal, Canada

zhounan@ucm.es, jlvilarz@ucm.es(∗ corresponding author), jose.garrido@concordia.ca,
aheras@ccee.ucm.es
Climate change encompasses long-term alterations in temperature, precipitation, sea levels, and other aspects of Earth’s system, presenting profound challenges to human society and the insurance industry. The
phenomenon’s growing impact is evident in the heightened frequency and severity of weather-related events
such as hurricanes, floods, and droughts, which consequently increase insurance claims. As traditional risk
assessment models become less reliable due to these changing patterns, the insurance sector is compelled torevise its methodologies to integrate climate change projections and assessments into their frameworks fora more accurate determination of premiums.
This adaptation is facilitated by tools like the Actuaries Climate Index™ (ACI), a significant index
developed collaboratively by leading actuarial societies in North America. The ACI provides a factual,neutral metric for observing climate change impacts through a set of climate variables that track extreme
weather events and sea-level changes. [1] This index has inspired similar initiatives globally, including theAustralian Actuaries Climate Index [2] and the Iberian Actuarial Climate Index (IACI), each tailored to their
specific regional climate data sets and challenges.[3]The IACI, in particular, leverages data from the ERA5-Land reanalysis dataset to monitor the Iberian
Peninsula’s climate trends. Unlike its North American counterpart, which is calculated for multiple subregions, the IACI utilizes a grid of 6,526 cells covering the Iberian Peninsula to provide a high-resolution
view of climate changes and their seasonal variations. This detailed granularity allows for a more nuanced
understanding of localized climate risks, which is crucial for insurance companies when assessing risks andsetting premiums in specific areas.

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Comparative analyses between the IACI and the ACI demonstrate consistent patterns of climate change
across these regions, affirming the reliability of these indices in capturing extreme climate phenomena. However, the data also highlight variations in extreme climate events across different sub-regions, necessitating
a localized approach to risk assessment. This insight is particularly important for insurance companies, as
it enables them to develop tailored insurance products and adjust premiums accurately according to specificclimate risks.
The impact of climate change varies between Spain and Portugal. Spain is becoming increasingly dry
and hot, with more frequent extreme climate events compared to Portugal. In contrast, Portugal’s Iberian
Actuarial Climate Index (IACI) suggests a slightly lesser impact from climate change than Spain. This
underscores the importance of considering national differences in climate risk assessments for the Iberian
Peninsula.
Looking forward, further research is needed to refine the IACI by possibly redefining its components
and improving the definition of grid cells and sub-regions. This will help bridge the gap between physicalclimate risks and their financial implications more effectively. The ultimate goal is to enhance the IACI’s
utility in the actuarial toolbox, aiding in the quantification and management of claims frequency, severity,and climate risk-adjusted premiums and reserves. Future advancements in this area are essential for the
insurance industry to keep pace with the escalating challenges posed by climate change.
Acknowledgements: The research conducted by the four authors was supported by the “Ayudas a la Investigación Ignacio H. de Larramendi” grant from Fundación MAPFRE (Spain). Prof. Jose Luis Vilar-Zanón
and Prof. Antonio Heras contributed to this research while funded by grants from the Spanish Government’s
Ministry of Science and Innovation, with grant numbers PID2020-115700RB-I00 and PID2021- 125133NBI00, respectively. Prof. Garrido kindly acknowledges the financial support of the Chaire d’Excellence Digital Insurance and Long term risk –DIALog (https://chaire-dialog.fr/).

References[1] ACI (2018) Actuaries Climate Index: Development and Design. American Academy of Actuaries,
Canadian Institute of Actuaries, Casualty Actuarial Society, Society of Actuaries.
[2] AACI (2003) Design Documentation: Australian Actuaries Climate Index. American Academy ofActuaries, Canadian Institute of Actuaries, Casualty Actuarial Society, Society of Actuaries.
[3] Zhou, N., Vilar-Zanón, J. L., Garrido, J., & Heras Martı́nez, A.-J. (2023) On the definition of an
actuarial climate index for the Iberian peninsula. Anales Del Instituto De Actuarios Españoles (29):37–
59.
[4] Garrido J, Milhaud X, Olympio A (2023) The definition of a French actuarial climate index; one more
step towards a European index. Preprint. https://hal.science/hal-04491982.

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Mathematical Finance 2
OPTION PRICING WITH GIVEN CONSTRAINTS AND ITS APPLICATIONTO LIFE INSURANCE CONTRACTS
Betty Guo1,∗ , Alexander Melnikov1
1 University of Alberta

betty2@ualberta.ca (∗ corresponding author), melnikov@ualberta.ca
The financial industry is a dynamic world filled with uncertainties. Risk management is the uttermost
concern for individuals, corporations, and institutions. Therefore, using hedging for pricing is prevalent infinancial mathematics to protect against movements of future outcomes. The standard approach of hedging
is to construct a portfolio of financial instruments that replicates the cash flow corresponding to the hedged
item. The primary objective of hedging through replication of cash flow of a contingent claim is to protect
against potential losses. Therefore, contingent claim priced though this approach does not allow for profit.
The theory of quantile hedging developed by Follmer and Leukert [3] provides an approach that maximizes the probability of a successful hedge with a reduced initial capital. Alternatively, one can define abound ϵ for chance of unsuccessful hedge and minimize the initial capital required such that the probability of successful hedge is at least 1 − ϵ. The quantile hedging concept does not allow for selection of theprobability of shortfall. Novikov [7] proposed an approach of hedging with a given probability in a complete market with one risky and one risk-free asset. Considering the approach by Novikov [7] we extend
this approach of hedging with a given probability into two-dimensional case and in terms of both diffusion
and jump-diffusion models [5]. Furthermore, this approach will be applied in the calculation of exchange
options that will be later applied to the pricing and hedging of life insurance contracts.
Equity-linked life insurance contracts combine life insurance protection with investment options tied tothe performance of specific equity or investment funds. They pay stochastic benefits linked to the movement
in a financial market while providing guaranteed benefits. The benefits are paid only if conditions are met
such as death or survival of policyholders. Therefore, equity linked insurance contract pricing are much
more complicated.
As mortality cannot be traded in any market, it is not possible to hedge mortality risk. Hence, theinsurance market is incomplete and perfect hedging is impossible. Applying quantile hedging to equity
linked insurance contracts allow for separation of financial risk and mortality risk. Brennan and Schwartz[2] and Boyle and Schwartz [1] were the first papers to discuss hedging of equity-linked insurance contracts.
The approach of reducing equity-linked insurance contracts to a call or put options and apply perfect hedging
is widely used today. We will follow the approach of Brennan and Schwartz and combine hedging with agiven probability to price and hedge an equity linked insurance contract.
The insurance contract under discussion is an equity-linked pure endowment contract. In such contracts,
the insureds receive the linked equity if they can survive a certain period (maturity.) In this research, we
assume there are one risk-free asset and two risky assets. We will consider a diffusion model generated
by two Wiener processes and with a correlation coefficient ρ as in the model by Margrabe [4]. For the
jump-diffusion model we will consider one Wiener process in which both risky asset prices are generated
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from.
In addition to partial hedging, we expand our study boarder to include efficient hedging. Partial hedging
with a given probability provides the investor a higher profit by allowing for some probability of a potential
loss. However, the amount of loss cannot be known beforehand or controlled. Considering this problem, wedevelop an approach that allows for hedging with a given expected loss based on Novikov’s [7] approach.
Furthermore, using Melnikov’s [6] development, efficient hedging is applied to pricing of equity linked
insurance contracts. Moreover, the theoretical findings are illustrated by numerical examples that are basedon real financial and actuarial data.
Acknowledgement: The research is supported by the Discovery Grant: NSERC RGPIN-2019-04922.

References[1] Boyle PP, Schwartz ES (1977) Equilibrium prices of guarantees under equity-linked contracts. Journalof Risk and Insurance 44:639–680.
[2] Brennan MJ, Schwartz ES (1976). The pricing of equity-linked life insurance policies with an asset
value guarantee. Journal of Financial Economics 3:195–213.
[3] Follmer H, Leukert P (1999) Quantile Hedging. Finance and Stochastics 3:251–273.
[4] Margrabe W (1978) The value of an option to exchange one asset to another. Journal of Finance
33:177–186.
[5] Melnikov AV (1996) Stochastic differential equations: singularity of coefficients, regression models
and stochastic approximation. Russian Mathematical Surveys 51:43–136.
[6] Melnikov AV (2004) Efficient hedging of equity-linked life insurance policies. Doklady Mathematics
69:462–464.
[7] Novikov A (1999) Hedging of Options with a Given Probability. Theory of Probability & Its Applications 43:135–143.

GANs FOR PORTFOLIO OPTIMIZATION
Ralf Korn1,2 , Laurena Ramadani1,2,∗
1 Department of Mathematics, RPTU Kaiserslautern-Landau, Kaiserslautern 67663, Germany
2 Department of Financial Mathematics, Fraunhofer ITWM, Kaiserslautern 67663, Germany

korn@mathematik.uni-kl.de, ramadani@mathematik.uni-kl.de (∗ corresponding author)
Generative Adversarial Networks GANs, first proposed by Ian Goodfellow in 2014 [1], are an excitingchange in the architecture of deep neural networks. They have achieved notable results in generating realistic data across various domains, such as producing real-looking images of human faces, translating one
image to another, for example, photos of summer to winter, or day-to-night, 3D image generation. Other
research areas, such as speech synthesis and video generation, have been analyzed along with images. An76

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other field in which the application of GANs has been explored is finance. For instance, QuantGANs [2]introduces utilizing temporal convolutional networks (TCNs) to approximate volatility and capture longrange dependencies between variables for generating time-series data. Further, S. Hyland used Recurrent
Conditional GANs in [3] to produce realistic synthetic medical data because of the limited access to medical reports due to privacy regulations. We often have too few data points and need more to develop robustmodels and algorithms. Privacy regulations and data access restrictions further aggravate this challenge.
With GANs, we can generate synthetic financial data that resembles real-world data, which we use to extend
limited historical data, train machine learning models, and conduct simulations for various financial applications. There are different types of GANs. In our study, we specifically utilized a kind of GAN known as
conditional GAN (cGAN). The objective was to model the probability distribution of one step ahead valueof the actual data set xt+1 . In our cGAN setup, we employed historical data as a condition x0 , x1 , ..., xt toestimate the conditional probability distribution p(xt+1 |c), where ’c’ represents the historical data used as
input.
In our research, we try to answer the question, “Can we use GANs for portfolio optimization?”. A crucial
task of portfolio optimization is to get the parameters of the securities, i.e., the means and covariances of the
returns of the stock prices. We use the log-increments of stock prices for Amazon, Apple, and Netflix anduse the trained GANs to generate more log-increments of the stock prices. In order to avoid missing out on
the correlations of the log returns, we perform a principal component analysis to get orthogonal components
from the joint log returns. Then, we build separate GANs for each component and use the trained GANs
to generate more realizations of the components. To estimate the parameters for portfolio optimization, we
transform the generated components back into log returns, and then we estimate the relevant parameters on
the complete data set and the generated data set only. Finally, we compare the performance of the different
portfolios based on the parameters estimated by traditional methods of standard training data and simulated
data by GANs. To see which data can be trusted more, the historical ones or the GAN-generated data, wetest with synthetic data where we know that the assumptions are satisfied. We consider different BlackScholes-type cases where our test data are synthetic data with (independent, pairwise correlated) log-normal
returns and the solution when maximizing the expected growth rate is known.
Generated data from GANs for Amazon, Apple, and Netflix - log returns resulted in superior performance in constructing both the minimum variance portfolio and the portfolio with the maximum Sharpe ratio. We used Markowitz’s Mean-Variance Approach for this analysis, comparing the outcomes with optimal
portfolios derived from standard training data. Additionally, when considering synthetic log-normal data,
the GANs perform consistently better regarding the optimal portfolio process. Notably, the GAN-generated
data are able to capture the volatility structure quite well. Although the volatility estimation works betteron the train data, this is compensated by the drift estimation on the GANs-generated data. Furthermore,
extending the time window of the generated data improved volatility estimation.

References[1] Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y(2014) Generative Adversarial Networks.
[2] Wiese M, Knobloch R, Korn R, Kretschmer P (2019) Quant GANs: Deep Generation of Financial
Time Series.

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[3] Esteban C, Hyland SL, Rätsch G (2017) Real-valued (Medical) Time Series Generation with Recurrent
Conditional GANs.

PERPETUAL AMERICAN OPTIONS IN A JUMP DIFFUSION MODELWITH TWO-SIDED JUMPS UNDER POISSON OBSERVATIONS
M.V. Boutsikas1 , D.-J. Economides1,∗
1 Dept. of Statistics and Insurance Science, Univ. of Piraeus, Greece.

mbouts@unipi.gr, davoik@unipi.gr (∗ corresponding author)
We investigate the problem of pricing Perpetual American put and call options under the assumption that theoption can be exercised only at random inspection times which are formulated by a Poisson Process. Employing an exponential Levy model for the price of the underlying asset, we specifically examine a jumpdiffusion model with two-sided jumps. We present key identities to express the option’s payoff and theexercise probability in terms of the undershoot/overshoot for the put/call scenarios. Additionally, we derive
explicit formulas for the payoff, time until exercise and optimal exercise policy under two conditions for the
log-price of the underlying asset: i) linear Brownian motion and ii) double exponential jump-diffusion process. Valuation under the risk-neutral probability measure is provided for both cases, along with asymptotic
formulas yielding well-established results from continuous-time models. Our numerical examples illustrate
the impact of inspection intensity on pricing outcomes for both scenarios.
Acknowledgement: This work has been partly supported by the University of Piraeus Research Center.

ACCELERATED COMPUTATIONS OF SENSITIVITIES FOR XVA
Griselda Deelstra1,∗ , Lech A. Grzelak2,3 , Felix L. Wolf1
1 Department of Mathematics, Université libre de Bruxelles, Brussels, Belgium
2 Mathematical Institute, Utrecht University, Utrecht, the Netherlands
3 Rabobank, Utrecht, the Netherlands

Griselda.Deelstra@ulb.be (∗ corresponding author), L.A.Grzelak@uu.nl, Felix.Wolf@ulb.be
For large financial institutions, such as banks and pension funds, most products are linear (without option
features) and are rather easy to evaluate. However, the calculation of xVA is very time-demanding due to themany transactions. This is particularly the case for portfolios with many long-term swaps. Indeed, exposure
simulations are fundamental to many xVA calculations and are a nested expectation problem where repeatedportfolio valuations create a significant computational expense.
Sensitivity calculations which require shocked and unshocked valuations in bump-and-revalue schemes
exacerbate the computational load. A known reduction of the portfolio valuation cost is understood to be78

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found in polynomial approximations, which we apply in this article to interest rate sensitivities of expected
exposures. We consider a method based on the approximation of the shocked and unshocked valuation
functions, as well as a novel approach in which the difference between these functions is approximated.
Numerical experiments with interest rate derivatives are conducted to demonstrate the high accuracy
and remarkable computational cost reduction, which could also be used for other problems in an insurance
and pension framework. In particular, we illustrate how the method can be extended to more general xVA
models using the example of CVA with wrong-way risk.

Data Science 2
LEVERAGING RELATIONAL DATABASES FOR SPATIAL ANALYSIS AND
DECISION MAKING IN INSURANCE
Luis Cespedes1,∗ , Miguel Santolino1 , Mercedes Ayuso1
1 Riskcenter-IREA

lcespeco7@alumnes.ub.edu (∗ corresponding author), msantolino@ub.edu, mayuso@ub.edu
This study focuses on the application of relational databases to better understand risk characteristics andassist in decision making to insurers. A relational database is a database whose logical structure is made up
of a collection of inter-related tables. The data volume has exponentially grown in last years in the world.
The use of relational databases that combine private internal data and public data sources can offer new
insights to insurers for a complete understanding of risks. To illustrate its usefulness, this paper will show
two fields where they can be used for a better understanding of risks.
Our first application of relational databases is focused on the degree of urbanization of the motor injury
accident. The riskiness of a driver is conditioned by the environment where he/she moves [1]. Population
density and its corresponding infrastructures not only heavily determines drivers’ maneuvers and behaviors,
but also the expected consequences of their mistakes [2, 3]. Several studies have shown that rural areas tend
to concentrate more crashes and more severe injuries in comparison to urban areas [4].
Incorporating these research topics into insurance companies’ models is important. However, adding
new variables to a model when they do not have clear-cut classifications increases the difficulty. Insurancecompanies are forced to choose between more variable customization or, when available, using standardized
criteria. There are situations where opting for homogeneous criteria offers certain advantages, it makes
market comparisons easier, and enables leveraging public available data if matched.
Using a relational data model that matches the postal code of the location of a claim or the residence of adriver to the degree of urbanization can give an edge to characterize more accurately these risks, in particularEurostat’s degree of urbanization methodology. The latter classification not only allows companies to know
the share of urban/suburban/rural drivers in the portfolio, to change their risk appetites and target desired
proportion, but also to find commonalities in crashes or claims by urbanization degree, such that someof them can be bundled and analyzed together by pricing and reserving departments. Furthermore, other79

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publicly available data could also be considered, such as the meteorology, and enrich our understanding.
These analyses open up a springboard to develop the skills needed to exploit telematics data in the future.
The second illustration combines the information of all passengers of a vehicle involved in a motor
injury accident. Insurance companies have access to many data sources and can analyze motor claims frommultiple perspectives. For claims in which different individuals are in the same insured vehicled, relevant
information is lost when insurers pay only attention to aggregated costs and do not consider the variations
coming from their injuries, especially when there is a recurrent pattern in the driver-passenger(s) profiles.
To analyze the insured risk as a whole, both in terms of pricing and reserving, it is important to consider the
injury heterogeneity in passenger vehicles. Rather than solely evaluating the total cost per vehicle for theclaim, a more nuanced analysis can be conducted. Understanding the heterogeneity in passenger injuries
could help claims and reserving teams to have a more tailored opening reserves that do not distort in excess
their quarterly average costs estimation.
Given that crashes represent the subset of policies of the company’s portfolio where the risk has materialized, crash reports are useful, not just to understand the claim, but also to infer traits of policyholders
that condition their risk. This involves estimating the conditional expected cost of the claim based on both
the driver’s characteristics and those of its expected passengers. For instance, if a crash occurred knowingthat the vehicle had only one passenger alongside the driver, an initial reserve for bodily injury could beestablished based on the expected probabilities of severity levels according to the number of passengers.
Alternatively, if the company wanted to estimate the total expected costs of bodily injury claims, it could
incorporate the expected probability that insured drivers will be accompanied by one or more passengers andthe estimated severity of injuries in each case. Matching all the tables can be easily done with a relational
database, where keys are matched to relate passengers or all occupants with crash characteristics, enablingdata manipulation and analysis. The composition inside the car varies and multiple combinations may beconsidered.
Acknowledgements: We are grateful to the Dirección General de Tráfico for access to their database. We
also are grateful to the Spanish Ministry of Science and Innovation grant PID2019-105986GB-C21 and to
the Departament de Recerca i Universitats, del Departament d’Acció Climàtica, Alimentació i Agenda Rurali del Fons Climàtic de la Generalitat de Catalunya (2023 CLIMA 00012).

References[1] Pljakic M, Jovanovic D, Matovic B (2022) The influence of traffic-infrastructure factors on pedestrian
accidents at the macro-level: The geographically weighted regression approach. Journal of Safety
Research 83:248–259.
[2] Abdel-Aty M, Lee J, Siddiqui C, Choi K (2013) Geographical unit-based analysis in the context oftransportation safety planning. Transportation Research. Part A, Policy and Practice 49:62–75.
[3] Keeves, J, Ekegren CL, Beck B, Gabbe BJ (2019) The relationship between geographic location andoutcomes following injury: A scoping review. Injury 50(11):1826–1838.
[4] Peura C, Kilch JA, Clark DE (2015) Evaluating adverse rural crash outcomes using the NHTSA State
Data System. Accident Analysis and Prevention 82:257–262.

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GEO-SPATIAL MODELLING OF VEHICLE CRIME IN NORTHERNIRELAND USING COMPUTER VISION T0 IDENTIFY ENVIRONMENTAL
FACTORS.
James Hannon1,∗ , Declan French2 , Barry Quinn2 , Adrian O’Hagan3
1 Centre for Research Training in Foundations of Data Science, University College Dublin
2 Queen’s Business School, United Kingdom
2 School of Mathematics and Statistics, University College Dublin

james.hannon1@ucdconnect.ie (∗ corresponding author), declan.french@qub.ac.uk,
b.quinn@qub.ac.uk, adrian.ohagan@ucd.ie
Insurers use postal codes to assess the level of risk associated with an area by pinpointing the exact locationsof certain losses, for example flood or theft. The main modelling assumption used is that the historical data
is a suitable indicator for future claims. There exists a wealth of literature hypothesizing that criminality
is influenced by environmental factors. As postal codes and historical data do not account for the reasons
why crimes occur, any changes to the environment that may enable or deter crime do not become accurately
priced into models in the short term. We propose that by finding indicators of the presence or absence ofcrime in street-level photographs, we can address why certain environments have greater levels of risk. As
the environment changes, we can better account for the fluctuating risk levels in areas.
To do this we accessed street level photographs via Google Street View (GSV). We used an open source
open-set object detector, called Grounding DINO [1], which detects user specified objects in images, andGemini [2], Google’s multimodal large language model. We applied Grounding DINO and Gemini to approximately 2 million images of Northern Ireland taken between 2022 and 2023. From the literature wefound that environmental indicators of vehicle crime include decay and dilapidation. We find signs of decay
and dilapidation by looking for broken windows, abandoned buildings, vacant sites, overgrown vegetation,
graffiti and litter in the street-level images. On the other hand, environmental deterrents to vehicle crime
include the presence of police, amenities, self-policing communities and surveillance devices. We findthese deterrents by searching for police stations, shop fronts and CCTV cameras. We identify self-policing
communities via the presence of paramilitary groups, who mark their territories through flags and murals.
Over the same time period we have publicly available street level vehicle crime data from the PSNI.
We assess the impact environmental factors have on vehicle crime through the use of geo-spatial models.
We account for confounding variables, such as socioeconomic status, and check for significant interactions
between variables such as policing and surveillance devices.
Acknowledgements: The first author acknowledges this work has emanated from research conducted withthe financial support of Science Foundation Ireland (SFI) under Grant Number SFI 18/CRT/6049 and theBritish Academy (BA)/Leverhulme Small Research Grants under Grant Number SRG2223/231522.

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References[1] Liu S, Zeng Z, Ren T, Li F, Zhang H, Yang J, Li C, Yang J, Su H, Zhu J, et al. (2023) Grounding dino:
Marrying dino with grounded pre-training for open-set object detection. arXiv:2303.05499.
[2] Team Gemini, Anil R, Borgeaud S, Wu Y, Alayrac J-B, Yu J, Soricut R, Schalkwyk J, Dai AM, Hauth
A, et al. (2023) Gemini: A Family of Highly Capable Multimodal Models. arXiv:2312.11805.

CHALLENGES IN ACTUARIAL LEARNING FOR LOSS MODELING OF
BRAZILIAN SOYBEAN CROPS
Helton Graziadei1,∗ , Eduardo F.L. de Melo1,2 , Rodrigo S. Targino1
1 School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro, Brazil
2 UERJ - State University of Rio de Janeiro, Brazil
3 SUSEP - Superintendence of Private Insurance, Rio de Janeiro, Brazil

helton.carvalho@fgv.br (∗ corresponding author), eduardo.melo@fgv.br, rodrigo.targino@fgv.br
The agricultural sector plays a fundamental role in Brazil’s economy, contributing approximately 25% to
the GDP in 2022, with agribusiness generating around 2.65 trillion BRL (475 billion USD). Sustained productivity is crucial, as any downturn directly impacts this vital economic sector. In 2022/2023, the plantedarea produced 312.5 million tons of grains, supplying both national and international markets. Soybean,
the predominant crop, reached an output of 153.6 million tons in 2023, aligning with the production of all
OECD nations combined. This underscores Brazil’s agricultural relevance amid global challenges like thewar in Eastern Europe, rising prices, inflation, and extreme weather.
Agricultural insurance is essential for mitigating financial risks faced by farmers due to adverse weather
and pests. It provides coverage against losses affecting insured crops, acting as a crucial safety net. The
loss ratio for crop insurance in Brazil reached 281.6% in the first half of 2022, up from 89.7% in 2021. This
sharp increase highlights the significant impact of adverse weather conditions on agriculture in regions suchas the south and middle-west of Brazil, leading to substantial losses in agricultural insurance and concerns
among insurers and reinsurers. The effects of global warming and climate change are increasingly apparent,
reflected in the higher frequency and severity of claims.
Given this context, the paper introduces predictive actuarial models designed to estimate insurance
losses for insured and subsidized areas, particularly focusing on soybeans. Utilizing databases from various sources, including the Ministry of Agriculture, the Climate Research Unit at the University of East
Anglia, the National Water Agency, and the Columbia Climate School, we incorporate meteorological data(precipitation and temperature), soil humidity, and El Niño/La Niña occurrence indices to enhance the accuracy of pricing and risk assessment.
The actuarial model aggregates data at the municipality level, defining the loss variable Lij as:
P
Li,j = P

SJ
k∈i Yk,j Sk

k∈i Ak,j Pk,j82,

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where Yk,j is the claim amount, Ak,j is the insured area, Pk,j is the insured crop yield, and SJ and Sk aresoybean spot prices at different dates.
The expected losses E[Lij | Xij ] are modeled using a two-stage hierarchy: a classification model forthe occurrence of claims and a regression model for the magnitude of losses. The hierarchical structure of
the data-generating process D = {(Xij , Zij , Lij ) : i = 1, . . . , nj , j = 1, . . . , J} is defined with nj being
the number of municipalities with a positive insured area in crop year j and J the total number of crop
years. Variables considered include latitude and longitude of the municipality, Available water capacity ofthe municipality, total precipitation (in mm), and average temperatures in November, December, January,
and February (the most relevant months for soybeans) and the Southern Oscillation Index (SOI) in a given
year.
Our primary goal is to predict expected
losses Lij based on covariates Xij . This is estimated by theconditional expectation E(Lij | Xij which can be factored, by the law of total expectation, as:





E Lij | Xij = E Lij | Xij , Zij = 1 · P Zij = 1 | Xij ,under the assumption that E(Lij | Xij , Zij = 0) = 0. This assumption states that if there are no claims inthe municipality i at crop year j, then the relative loss is zero.
We begin by fitting a classification model for Zij given Xij , using the entire dataset. Next, we fit a
regression model for Lij restricted to instances where Zij = 1. This two-stage model hierarchy includes:
Zij | Xij ∼ Fij
Lij | Zij , Xij ∼ Gij
We then present several choices for the two-stage hiearchy, consisting of generalized linear models,
generalized additive models, and tree-based models. Also, to understand in greater detail the marginalcontribution of each weather variable on the predictive loss model, we explore partial dependence plots[1, 2].
Finally, we conduct a stress test on the climate variables to understand how the model performs under
several environmental scenarios. The procedure starts by setting a stress criterion which is used to imputevalues that simulate extreme climate conditions for the 2021/2022 crop year.
Results are pertinent for public policy, including federal subsidies and the design of agricultural catastrophe funds. By improving risk assessment and pricing accuracy, these models contribute to the agricultural
sector’s resilience against climatic challenges, ensuring stability and growth. Specifically, they address theneed for risk estimation models in the face of increased loss ratios, providing insights crucial for both theBrazilian population and the global community given the significant role of grain production in the global
supply chain.

References[1] Friedman J (2001) Greedy function approximation: a gradient boosting machine. Annals of statistics
1189–1232.
[2] Zhao QE, Hastie T (2021) Causal interpretations of black-box models. Journal of Business & Economic Statistics 272–281.
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EFFICIENTLY COMPUTING ANNUITY CONVERSION FACTORS VIAFEED-FORWARD NEURAL NETWORKS
Maria Aragona1 , Sascha Günther2 , Peter Hieber2,∗
1 University of Torino
2 University of Lausanne (HEC Lausanne)

peter.hieber@unil.ch (∗ corresponding author)
Many pension plans and private retirement products contain annuity factors, converting the funds at somefuture time into lifelong income. In general model settings like for example the Lee-Carter mortality model,
analytical values for the annuity factors are not available and one has to rely on numerical techniques. Theircomputation typically requires nested simulations as they depend on the interest rate level and the mortality
tables at the time of retirement. We exploit the flexibility and efficiency of feed-forward neural networks
to value the annuity factors at the time of retirement. In a numerical study, we compare our deep learning
approach to (least-squares) Monte-Carlo that can be represented as special cases of the neural network.

References[1] Aragona M, Günther S, Hieber P (2024) Efficiently Computing Annuity Conversion Factors via FeedForward Neural Networks. Available at SSRN 4696751.
[2] Bacinello AR, Millossovich P, Viviano F (2021) An Efficient Monte Carlo Based Approach for the
Simulation of Future Annuity Values. DEAMS Research Paper Series No. 2.
[3] Fernandez-Arjona L (2021) A neural network model for solvency calculations in life insurance. Annalsof Actuarial Science 15(2):259–275.
[4] Jonen C, Meyhöfer T, Nikolić Z (2023) Neural networks meet least squares Monte Carlo at internal
model data. European Actuarial Journal 13(1):399–425.

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Life Insurance 2
RMOps: A ROBUST FRAMEWORK FOR MITIGATING BIAS AND
VARIANCE IN MORTALITY PREDICTION IN LIFE INSURANCE
Chia-Chih Chao1∗ , Yu-Kai Huang1 , Chia-An Wang1 , Po-Hua Lai1 , Fang-Chi Chang1 ,Chin-Jung Yeh1 , Yun-Tuan Chang1 , Yu-Chen Lee1 , Chiao-Ching Huang1 , Shu-Yi Chuang1
1 CathayLife Insurance Taipei, Taiwan

qqcat1@cathaylife.com.tw (∗ corresponding author), ykhuang@cathaylife.com.tw,joanxwang@cathaylife.com.tw, chrislai@cathaylife.com.tw, fangchi@cathaylife.com.tw,cjyeh@cathaylife.com.tw, eveyun829@cathaylife.com.tw, yuclee@cathaylife.com.tw,chiaoching@cathaylife.com.tw, shuyi@cathaylife.com.tw
In the life insurance industry, insurers strive for more precise and robust risk ratings by employing complex models in the underwriting process. However, if these predictions are subject to bias and variance,
they can lead to inappropriate risk assessments, potentially incurring significant costs in underwriting. This
study focuses on mortality rates of customer segments. We introduce the Risk-rating Modeling Operations(RMOps), a framework that rigorously assesses the robustness of models. The development of RMOps
stemmed from a series of rigorous experiments aimed at evaluating the robustness of various modelingtechniques. These experiments revealed that three main components impacted the overall performance ofthe models: (1) Ensuring the number of model samples is sufficient (in mortality prediction, the data isunbalanced); (2) Selecting the best model with multiple performance (short, medium, and long-term mortality rates); (3) Avoiding the overestimation or underestimation of model results. Our study demonstrates
that RMOps maintains average monthly incidence rate variances below 5% in the high-risk segment overan eight-year period. Additionally, the Kolmogorov-Smirnov test reveals no significant difference between
the monthly incidence rates in the high-risk segment and a normal distribution. RMOps provides a robust
framework for enhancing risk-rating models, enabling the life insurance industry to implement more accurate underwriting processes with confidence. And by using RMOps, our risk-rating model facilitates theimplementation of randomized medical testing for the high-risk client segment, resulting in a 30% monthly
increase in the hit rate of high-risk physical examinations over a year without the need for model retraining.
Keywords: Data science · Life insurance · Mortality rates · Model robustness · Bias and variance · Risk
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RISK ADJUSTMENT MODELING FOR LONGEVITY RISK
D. Rodrigues1,∗ , A. Moura1,2
1 CEMAPRE - Mathematics Applied to Forecasting and Economic Decision & REM - Research in

Economics and Mathematics
2 ISEG - Lisbon School of Economics and Management, University of Lisbon

dfj. rodrigues @ aln.iseg.ulisboa.pt (∗ corresponding author), amoura @ iseg.ulisboa.pt
In recent years, the insurance sector has been adopting new regulations to standardize financial, actuarial andaccounting reporting processes with the purpose of assessing and comparing the performance of insurancecompanies. This is the case of IFRS 17 - Insurance Contracts, published in 2017 by the IASB, which is
being implemented worldwide. Its implementation presents numerous challenges for insurance companies,
one of which is the determination of the Risk Adjustment (RA), given that the standard does not prescribe
any particular methodology.
The Cost-of-Capital (CoC) and quantile techniques using simulation are the two main methodologies
to calculate the RA. This is because these are well-known and widely used methodologies in the insurance
sector, already applied in several companies prior to the implementation of IFRS 17. However, both methods have significant drawbacks: the lack of sensitivity to the portfolio’s historical characteristics and theapplication of fixed shocks, in the case of the CoC technique; or the time consuming nature of simulations,in the case of quantile techniques.
In this work, an original model is proposed for the calculation of the RA for longevity risk in life
insurance. We use well-known techniques from the theory of convex ordering of random variables andcomonotonicity to devise analytical expressions to compute the RA for the total portfolio. We derive areasonable approximation and a boundary interval such that the lower bound is the approximation and theupper bound is the worst case scenario for the RA.
By using data inspired on a real life insurance portfolio of a leading company operating in Portugal, it
is shown that this model, which focuses on the volatility of the historical behavior of the portfolio in termsof exposure and deaths, results in a reliable approximation of the RA. Results are compared with the twoclassical techniques, demonstrating to have good characteristics.
Acknowledgement: The authors acknowledge financial support from FCT–Fundação para a Ciência e Tecnologia (Portugal), national funding, through research grants EXPL/EGE-ECO/0886/2021 and
UIDB/05069/2020.

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BASIC PERFORMANCE METRICS FOR LONGEVITY-LINKED
ANNUITANTS
Annamaria Olivieri1
1 Department of Economics and Management, University of Parma, Italy

annamaria.olivieri@unipr.it
The understanding of the actuarial principles on which the pricing and reserving process of life-contingent
benefits is based may be out of the reach of many individuals. This is particularly true when the benefit
amount is linked to random parameters, such as financial returns or mortality rates. A poor understanding of
the content and potential benefits of the insurance product may partially explain the low propensity to someinsurance coverages.
We focus on life insurance, and post-retirement benefits in particular. We suggest an intuitive way
to describe the reserving process, based on the information accessible (either directly or via proxy) to theindividual, namely the policy reserve amount, financial returns and a mortality/longevity index. Specifically,
we reinterpret the reserving (and, ultimately, the pricing) process in terms of equivalent periodic fees, which
represent a performance metric that can be grasped also by those who lack the ability to process complex
assessments. Finally, we investigate what insights, and design tips, can be gained for the particular case of
longevity-linked survival benefits.

IMPROVING SURVIVAL RATE ESTIMATES USING
INSURED AMOUNTS
Andrey Ugarte Montero1,∗ , Torsten Kleinow1 , Frank van Berkum1 , Michel Vellekoop1
1 Research Center for Longevity Risk, University of Amsterdam

a.d.ugartemontero@uva.nl (∗ corresponding author), t.kleinow@uva.nl,
f.vanberkum@uva.nl, m.h.vellekoop@uva.nl
Insurance companies need statistical tools to adequately assess the risk associated with their liabilities. In thelife insurance industry in particular, survival modeling is key to accurately assessing the value of insurance
policies and annuity business. Traditional techniques, however, emphasize individual survival over time,
regardless of the impact that an individual death may have on liabilities based on their sum insured. As aresult, practitioners have resorted to different methods to account for the fact that discrepancies between
actual and expected survival of individuals with higher sum insured may be more critical to a company’s
liabilities than those of individuals with lower benefits. In the Dutch industry, it is common to use insured
amount-weighted mortality by “observed” experience factors (see, for example, [2]); however, only age
and gender are typically used in the risk profile of policyholders under this methodology, enhancing theimportance of additional knowledge of techniques that allow multiple covariates. Another typical approach
used in the industry to deal with this is to develop insured amount-weighted survival models. Papers such87

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as [3] and [1] have described this practice as “ad hoc”, with [1] suggesting that annuity amounts be used asa covariate rather than a weight. In this context, using insured amount-weighted mortality is possible in theinsurance industry, and a thorough academic analysis of such weighted models, their theorical foundations,and their implications on the insurance industry appears to be lacking.
Our research focuses on formalizing and analyzing in depth some of the methods that can be used in
the insurance industry to account for the role of the sum insured in developing survival models. As partof the study, we use a new dataset with survival information of individuals buying annuity products in the
Netherlands to investigate how weighing observations with the sum assured or pension benefit will impact mortality estimates and financial predictions. We focus on both well-established techniques based on
maximum likelihood estimation with classical mortality laws and generalized linear (additive) models, allowing us to account for multiple risk factors and enabling us to set more granular assumptions that may be
relevant for pricing and reserving. To test this we use real life covariates available in our dataset. Weighing observations to compute parameter estimates using such models does not appear to raise major issues
from a theoretical perspective. The motivations, practical challenges, and consequences of such practice inthe life insurance industry deserve deeper analysis to understand the implications of their use in financial
estimations.

References[1] Pitacco E, Denuit M, Haberman S, Olivieri A (2009) Modelling longevity dynamics for pensions andannuity business. Mathematics texts from Oxford University Press.
[2] Plat R (2009) Stochastic portfolio specific mortality and the quantification of mortality basis risk.
Insurance: Mathematics and Economics 45(1):123–132.
[3] Richards SJ (2008) Applying Survival Models to Pensioner Mortality Data. British Actuarial Journal
14(2):257-303. ISSN 1357-3217.

PARALLEL SESSIONS V
Life Insurance 3
RISK MANAGEMENT IN THE RETIREMENT DECUMULATION PHASE
Alexandra Dias1
1 University of York, U.K.

alexandra.dias@york.ac.uk
The world population is getting older and consequently it is becoming more difficult for the active workforce
to support an increasingly growing older population. Due to these factors, among others, there has beena progressive move from defined benefit to defined contribution pension schemes. This means that, the88European Actuarial Journal Conference 2024
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responsibility of managing longevity risk and its financial implications is being moved from the State to
the individual. In this project, I focus on the problem of managing the risk in the decumulation phase, i.e.,during the period of retirement. Risk can be reduced to a minimum by buying a whole life annuity productbut that is extremely expensive and the return (in this case the pension) will be low. At the other end of therisk spectrum, the individual might opt to withdrawing all her pension pot (with tax implications) and invest
in the financial market aiming at maximizing returns at a much higher financial and longevity risk. This
research explores strategies between these two extremes of risk taking.

VALUING LIFE INSURANCE POLICIES WITH STOCHASTICALLYCORRELATED INTEREST RATES AND MORTALITY
Massimo Costabile1,∗ , Emilio Russo1 , Alessandro Staino1
1 University of Calabria

massimo.costabile@unical.it (∗ corresponding author), emilio.russo@unical.it, alessandro.staino@unical.it
We consider the problem of computing the fair value of life insurance policies when the evaluation framework is characterized by two stochastically correlated random variables. In particular, we consider two
diffusion processes describing the evolution of the short rate and of the intensity of mortality whose correlation is itself stochastic and it is described by a bounded Jacobi process. In order to compute the fair valueof the contract we propose a binomial tree based model to approximate the evolution of each process andthe, we merge together the univariate lattices to obtain the trivariate model being able to manage the pricing
problem. Extensive numerical experiments evidence that the proposed model is computationally efficientand produces accurate values.

PERFORMANCE PROFILES OF PROFIT SHARING INSURANCECONTRACTS WITH RETURN TARGET FINANCIAL STRATEGY UNDERIFRS 17
Barbara Rogo1
1 Department of Statical Sciences, Sapienza University of Romebarbara.rogo@uniroma1.it
This research examines the performance of an insurance company under the new accounting Standard, IFRS
17, with a specific focus on the Italian life insurance market. The new Standard introduces new financial
metrics and performance indicators. In particular, the profit from insurance business is quantified by theContractual Service Margin (CSM), representing the unearned profit released over the insurance group’s
lifetime as insurance services are delivered. Conversely, any losses, measured by the Loss Component (LC),are promptly recognized (see Palmborg et al. [7] and Yousufet al. [8]).
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A relevant component of the Italian life insurance portfolios is represented by Profit Sharing (PS) insurance products, which feature a cliquet-style guarantee (see e.g. De Felice and Moriconi [5]). The premiums
are invested in an asset portfolio whose annual return reassesses the insurance benefits through a distribution
mechanism. It is noteworthy that the portfolio return, pivotal for insurance cash flows, is calculated basedon book values, with a portion contractually mandated and not subject to discretion. The accounting rule
results in a portfolio return that is less variable compared to a market-based rule, as it reduces exposure tomarket volatility.
To comply with Standard requirements for this type of insurance contracts, which include market-based
valuation and the application of the Variable Fee Approach to adjust the CSM and LC, a stochastic model isnecessary. This model is used to describe the future evolutions of financial risk drivers, stemming from theasset portfolio, as well as actuarial risk drivers. The financial stochastic component incorporates stochastic
processes for the asset portfolio, comprising three main asset classes (bonds, stocks and investment funds).
Each asset class consists of various types of assets that directly impact the insurance cash outflows (seeIVASS [6]). These processes encompass the risk-free spot rate, credit spreads (see Brigo and Mercurio [3]),stocks, and investment funds, each described by a diffusion process in a stochastic differential equation
known as the Economic Scenario Generator (ESG). Changes in the rating of a bond issuer, resulting fromupgrades or downgrades, are also accounted for using a discrete-time Markov chain to model the stochastic
process of credit rating. To generate financial scenarios, a simulation numerical algorithm is applied, accurately replicating the financial strategy with which the asset portfolio is managed and taking into accountthe book asset values. The academic literature often models this as a percentage of the market value [2].
Alfonsi et al. [1] introduce a synthetic asset-liability model that considers both market and book values with
two sources of financial uncertainty. We grapple with managing additional financial uncertainties typicalof an asset portfolio managed by an Italian insurance company. The financial strategy, based on financial
and operational choices and rules set forth by the Administrative Board, aims to achieve a proper annual return consistent with the company’s risk appetite and tolerance. The risk-neutral probability measure is used
to project insurance cash flows consistently with the risk-free yield curve. Additionally, a liquidity factor,
accounting for the liquidity characteristics of insurance cash flows and adjusting the risk-free rates, is estimated using an approach similar to that used to calculate the Volatility Adjustment (VA) under the Solvency
II Directive. The actuarial stochastic component describes the uncertainty associated with mortality forces
by applying the Lee-Carter model within a Poisson setting to generate mortality scenarios (see Brouhns etal. [4]). In this setting, the CSM and LC are discrete-time random processes whose values evolve dependingon the variable fee. Specifically, the Standard considers the asset portfolio held by the insurance company
on behalf of the policyholder, from which it receives only a variable remuneration, known as the variable
fee. Since financial information is also related to insurance services, any changes in the variable fee amountover a 1-year period due to changes in financial and actuarial information are considered new profit or loss
and adjust the CSM or LC accordingly.
We explore how Profit Sharing (PS) insurance contracts can be aggregated into groups to meet Standard
requirements. Three performance profiles (onerous, profitable, and undecided) are associated and analyzed
under two distinct market scenarios (a low-interest-rate environment and a high-interest-rate environment).
We examine the influence of accounting rules and financial strategy on the performance. Additionally, weoffer insights that are useful for planning new business.

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References[1] Alfonsi A, Cherchali A, Infante Acevedo JA (2010) A synthetic model for asset-liability management
in life insurance, and analysis of the SCR with the standard formula. European Actuarial Journal
10(3):457–498.
[2] Bauer D, Bergmann D, Kiesel R (2010) On the risk-neutral valuation of life insurance contracts withnumerical methods in view. Astin Bullettin 40(1):65–94.
[3] Brigo D, Mercurio F (2001) A deterministic-shift extension of analytically-tractable and timehomogeneous short-rate models. Finance Stochast 5:369–387.
[4] Brouhns N, Denuit M, Vermut JK (2002) A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables. Insurance: Mathematics and Economics 31(3):373–393.
[5] De Felice M, Moriconi F (2005) Market based tools for managing the life insurance company. Astin
Bulletin 35(1):79–111.
[6] Istituto per la Vigilanza sulle Assicurazioni (2023) Bollettino Statistico. Gestioni Separate Vita (20172022).
[7] Palmborg L, Lindholm M, Lindskog F (2021) Financial position and performance under IFRS 17.
Scandinavian Actuarial Journal 2021(3):171–197.
[8] Yousuf W, Stansfield J, Malde K, Mirin N, Walton R, Thorpe B, Thorpe J, Iftode C, Tan L, Dyble R,
Pelsser A, Ghosh A, Qin W, Berry T (2021) The IFRS 17 contractual service margin: a life insurance
perspective. British Actuarial Journal 26(e2):1–105.

GENERAL BOUNDS FOR FUNCTIONALS OF THE LIFETIME,COMPATIBLE WITH LIFE TABLES
Mark Van Lokeren1
1 Imperial College London, United Kingdom

m.van-lokeren@imperial.ac.uk
In life insurance, life tables are used to estimate the survival distribution of individuals from a certain population. The tables only provide survival probabilities at integer values. Information about the distribution ofdeaths between two consecutive integer values is not available.
Many actuarial quantities are functionals of the lifetime, and computing them requires full information
about the lifetime. A possible solution to this problem is the introduction of fractional age assumptions.
However, the results of these computations depend strongly on the assumptions, which makes it quite difficult to compare them to each other. How good are they?
In this talk, we propose upper and lower bounds for actuarial quantities which hold for any fractional
age assumption. Moreover, we obtain these bounds using a general method.
Our method draws on optimal control, in particular Pontryagin’s maximum principle. As the method91

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does not rely on any other assumptions, the obtained bounds are the most general one can obtain using theavailable information. We also show that the bounds are sharp and provide an example of a lifetime that
achieves them.
To the best of our knowledge, this is the first time that techniques from optimal control are applied in
the context of life tables.

Nonlife Insurance Mathematics 3
PLUVIAL FLOOD RISK MODELLING USING FLOOD RISK MAPS AND
AN ADVANCED STOCHASTIC WEATHER GENERATOR: THE CASE OF
AUSTRIA
Hansjoerg Albrecher1 , Erwan Koch2 , Alaric J.A. Müller1,∗ , Nadav Peleg3
1 Actuarial Sciences department, University of Lausanne, Switzerland
2 Expertise Center for Climate Extremes, University of Lausanne, Switzerland
3 Institute of Earth Surface Dynamics, University of Lausanne, Switzerland

hansjoerg.albrecher@unil.ch, erwan.koch@unil.ch,alaric.muller.1@unil.ch (∗ corresponding author), nadav.peleg@unil.ch
Floods account for a significant portion of insurance losses resulting from natural hazards, and modelingthese losses is challenged by complex spatial dependence patterns. While existing literature on flood risk
often focuses on fluvial floods, floods triggered by heavy rainfall can also result in substantial insurance
losses. In this paper, our objective is to model pluvial flood losses stemming from extreme rainfall events.
We utilize the advanced stochastic weather generator for simulating 2-D high-resolution climate variables(AWE-GEN-2d) developed by Peleg et al. [4], to simulate high-resolution rainfall random fields. Focusing
on one or more spatial regions, we develop monthly models to capture spatially and temporally dependent
rainstorms through random fields. The AWE-GEN-2d model offers a robust framework for simulating suchstorms, enabling assessment of both the severity and frequency of pluvial flood losses in the regions underconsideration. In the spirit of Albrecher et al. [1], we demonstrate this methodology using Austria as acase study. Following the approach of Bernard et al. [2], the country is divided into distinct regions basedon clustering techniques applied to daily rainfall maxima. Several weather regions emerge as independent
clusters, for which we estimate expected losses due to pluvial floods. To achieve this, simulations exceedinga given precipitation return level, such as the one in one-hundred years return level, are employed to identify
locations prone to pluvial floods. To estimate losses due to pluvial floods in these locations, we propose
a functional relationship between simulated extreme rainfall and resulting flood levels for different returnlevels. The simulated water depth in flooded locations is then utilized to estimate insurance losses through adamage function approach. The latter enables modelling of flood losses associated with extreme rainstorms
for each region considered, while also providing insights into spatial diversification to enhance flood risk
resilience.
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References[1] Albrecher H, Kortschak D, Prettenthaler F (2020) Spatial Dependence Modeling of Flood Risk Using
Max-Stable Processes: The Example of Austria. Water 12(6):1805.
[2] Bernard E, Naveau P, Vrac M, Mestre O (2013) Clustering of Maxima: Spatial Dependencies among
Heavy Rainfall in France. Journal of Climate 26(20):7929–7937.
[3] Breinl K, Lun D, Müller-Thomy H, Blöschl G (2021) Understanding the Relationship between Rainfall
and Flood Probabilities through Combined Intensity-Duration-Frequency Analysis. Journal of Hydrology 602:126759.
[4] Peleg N, Fatichi S, Paschalis A, Molnar P, Burlando P (2017) An advanced stochastic weather generator
for simulating 2-D high-resolution climate variables. Journal of Advances in Modeling Earth Systems
9(3):1595–1627.

CREDIBILITY DISTRIBUTION ESTIMATION IN A HIERARCHICAL
FORM
Georgios Pitselis1
1 University of Piraeus

pitselis@unipi.gr
Very often in insurance practice the data has a hierarchical form and individual risks are classified according
to a hierarchical structure. Thus, one risk factor of the portfolio is divided into different subgroups, with
common features and subgroups into contracts with homogeneous risks and therefore we have to examinechanges at different points of the distribution with data, in a hierarchical form. In addition, hierarchical credibility distribution estimators are also established and numerical illustrations with insurance and financial
data are herein presented.
Acknowledgement: This work has been partly supported by the University of Piraeus Research Center.

References[1] Bozikas A, Pitselis G (2020) Multi-Population Mortality Modelling and Forecasting: A HierarchicalCredibility Regression Approach. European Actuarial Journal 11:231–267.
[2] Bühlmann H, Gisler A (2005) A Course in Credibility Theory and its Applications. Springer.
[3] Frees EW, Valdez E (2008) Hierarchical insurance claims modelling. Journal of the American Statistical Association 103(484):103–484.
[4] Jewell WS (1975) The use of collateral data in credibility theory: A hierarchical model. Giornale dell
Istituto Italiano degli Attuari 38:1–16.
[5] Jewell WS (1974) The Credible distribution. ASTIN Bulletin 3:237–269.
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[6] Pitselis G (2023) Weighted Credibility Distribution Estimation with Applications to Insurance andFinance. Risks 12(10):1–27.
[7] Pitselis G (2020) Quantiles in a multiple-stage nested classification credibility. European Actuarial
Journal 10:399–423.

MULTIVARIATE CLAIM COUNT REGRESSION MODEL WITH VARYINGDISPERSION AND DEPENDENCE PARAMETERS
Himchan Jeong1,∗ , George Tzougas2 , Tsz Chai Fung3
1 Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada
2 Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, UK
3 Department of Risk Management and Insurance, Georgia State University, Atlanta, GA, USA

himchan jeong@sfu.ca (∗ corresponding author), george.tzougas@hw.ac.uk, tfung@gsu.edu
The aim of this paper is to present a regression model for multivariate claim frequency data with dependence structures across the claim count responses, which may be of different sign and range, and overdispersion from the unobserved heterogeneity due to systematic effects in the data. For illustrative purposes, weconsider the bivariate Poisson-lognormal regression model with varying dispersion. Maximum likelihood
estimation of the model parameters is achieved through a novel Monte Carlo expectation–maximization
algorithm, which is shown to have a satisfactory performance when we exemplify our approach to Local
Government Property Insurance Fund data from the state of Wisconsin.

GED SPLINE ESTIMATION OF MULTIVARIATE ARCHIMEDEAN
COPULAS BASED ON THE WILLIAMSON D-TRANSFORM
Jaap Spreeuw1,∗ , Dimitrina S. Dimitrova1 , Vladimir K. Kaishev1
1 Bayes Business School, City, University of London

j.spreeuw@city.ac.uk (∗ presenting author), D.Dimitrova@city.ac.uk, Vladimir.Kaishev.1@city.ac.uk
Archimedean copulas have become a very popular way of modeling dependence between random variables
in actuarial science and finance, partly due to their mathematical tractability. McNeil and Nešlehová (2009)
have derived the exact conditions that need to be satisfied by a function, in order for it to be a valid generatorof an Archimedean copula for a particular dimension. They have also discovered an important stochastic
representation of the multivariate Archimedean copula as a survival copula of a simplex distribution, withthe generator being the Williamson transform of radial random variable. With this representation, Genest
et al. (2011) derive a nonparametric estimator of an Archimedean copula by reconstruction of the radial
part of the simplex distribution from the Kendall distribution function. Our aim in this paper is to introduce
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a novel estimator of the generator based on its Williamson transform, replacing the c.d.f. of the radial
random variable with a smoother, quadratic spline estimate. The latter is obtained applying the GeDS
(Geometrically Designed Splines) smoothing methodology of Kaishev et al. (2016). Some of the main
advantages of this approach are that: 1) it allows to approximate infinitely closely the underlying distributionof the radial random variable, and therefore the generator, for arbitrarily distributed, discrete, mixed, or
continuous radial random variables with no atom at zero; 2) it leads to a closed form expression for thegenerator, and therefore to a fast and accurate evaluation of it, as well as the copula, for an arbitrarily
distributed radial random variable and copula dimension. Th proposed procedure for fitting a GeD spline tothe corresponding empirical c.d.f. of the radial random variable, and obtaining an estimator of the generator,
and therefore the copula, is given. For two different Archimedean families (one with a continuous, theother one with a discrete radial random variable) the performance of the proposed estimator is illustrated forvarious combinations of dimension and number of observations.

References[1] Genest C, Nešlehová J, Ziegel J (2011) Inference in multivariate Archimedean copula models. TEST
20:223–256.
[2] Kaishev VK, Dimitrova D, Haberman S, Verrall R (2016) Geometrically designed, variable knot regression splines. Computational Statistics 31:1079–1105.
[3] McNeil AJ, Nešlehová J (2009) Multivariate Archimedean copulas, d-monotone functions and l1 norm
symmetric distributions. The Annals of Statistics 37(5B):3059–3097.

Health Insurance
DEVELOPMENT OF MULTIMORBIDITY PATTERNS IN OLDER ADULTS
IN SWITZERLAND: A COMPETING RISKS MODELING APPROACH
Laura Iveth Aburto Barrera1,∗ , Joachim Marti2 , Anna Nicolet2 , Joël Wagner1,3
1 Department of Actuarial Science, Faculty of Business and Economics (HEC), University of Lausanne,

Lausanne, Switzerland
2 Center for Primary Care and Public Health (Unisanté), University of Lausanne, Lausanne, Switzerland
3 Swiss Finance Institute, University of Lausanne, Switzerland

lauraiveth.aburtobarrera@unil.ch (∗ corresponding author), joachim.marti@unisante.ch,anna.nicolet@unisante.ch, joel.wagner@unil.ch
Multimorbidity, the co-occurrence of two or more chronic diseases in one person, is a complex challengethat affects individuals, healthcare systems and society. People with multimorbidity have a poorer qualityof life, a higher mortality rate and more hospitalizations and doctor visits than people with a single disease,95

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leading to higher health insurance costs. Our paper aims to investigate the progression of multimorbidity
by identifying the main disease patterns in the adult population. Using a novel dataset comprising thehealth insurance claims of 362 750 policyholders of one of the largest health insurers in Switzerland, wecategorize 22 chronic long-term diseases into 14 different pharmacy cost groups (PCGs) based on a robust
medical classification system [3] to assess the morbidity status of policyholders.
We focus on the development of multimorbidity and consider the transitions from one health state toanother or to death, as we are interested in the specific condition that occurs and the time spent in the statewith the pre-existing diseases. Developing on a competing risks framework [1] for multimorbidity, wherecompeting risks are the conditions (disease or death) that occur prior to a disease of interest, the model
considers K possible conditions, including K − 1 diseases in D = {d1 , . . . , dK−1 } and death dK . The
complete set of possible conditions is denoted by K = D ∪ {dK }. We therefore consider transitions with aunit increase in the number of diseases or death. We use di ⊂ D, i = 1, 2, . . . , K − 1 to denote the initialstate of an individual, where |di | = i, and i is the number of prevalent diseases. Furthermore, di+1 ⊂ K is thesubsequent state in which an additional disease or death occurs. The respective competing risks framework
corresponding to the transition from di to di+1 is depicted in Figure 1.
State di+1 ⊂ K
di ∪ {d1 }State di ⊂ Dwith |di | = i

di ∪ {d2 }didi ∪ {dK−1 }{dK }Figure 1: Illustration of the transition from di to di+1 in the competing risks framework.
In addition, we treat the left-censored observations, i.e., records in which an individual was diagnosed
with PCGs before entering the study so that the exact duration spent in state di is not observed, by usinga modified imputation method. We also handle some special cases in our data where individuals in thesubsequent state report not a one-unit increase but a two-unit increase in the number of diseases. To this end,
we develop an algorithm to simulate the next PCG when two additional PCGs are reported in the individualin the next state. Finally, we use subdistribution hazard models [2] adjusted for age effects to model key
multimorbidity patterns, taking into account the most common chronic diseases in the Swiss population.
Our analysis focuses on estimating the cumulative incidence functions for gender-specific multimorbidity
patterns depending on the initial diagnosis. By shedding light on these patterns, our study contributes toa deeper understanding of multimorbidity dynamics. It provides information for prevention strategies and96

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enables more targeted interventions to reduce both disease burden and economic impact.

References[1] Beyersmann J, Schumacher M, Allignol A (2012) Multistate modelling of competing risks. In: Competing Risks and Multistate Models with R. Springer, New York, NY.
[2] Fine JP, Gray RJ (1999) A Proportional Hazards Model for the Subdistribution of a Competing Risk.
Journal of the American Statistical Association 94(446):496–509.
[3] Huber CA, Szucs TD, Rapold R, Reich O (2013) Identifying patients with chronic conditions using
pharmacy data in Switzerland: an updated mapping approach to the classification of medications. BMC
Public Health 13:1030.

SOCIOECONOMIC BENEFITS OF THE BRAZILIAN INSS ATESTMEDPROGRAMME
Renata G. Alcoforado1,3,4,∗ , Hudo L.S.G. Alcoforado2 , Pedro A. Tenório1 , Alfredo D. Egı́dio dos
Reis3 , Alessandro A. Stefanutto4 , André P.F. Fidelis4
1 Department of Accounting and Actuarial Science, Universidade Federal de Pernambuco, Recife - Brazil
2 Department of Computer Science, Universidade Federal Rural de Pernambuco, Recife - Brazil
3 CEMAPRE & ISEG, Universidade de Lisboa, Lisboa – Portugal
4 INSS - National Social Security Institute, Brası́lia - Brazil

alcoforado.renata@ufpe.br (∗ corresponding author), hudo.leonardo@ufrpe.br, pedro.augustot@ufpe.br
alfredo@iseg.ulisboa.pt, alessandro.stefanutto@inss.gov.br, andre.fidelis@inss.gov.br
This study analyses forecast modeling with time series to project INSS expenses related to the AtestMed
programme, a recent socioeconomic initiative by the Brazilian government to streamline benefit compensation for temporary disability within the Social Security System. Aiming to reduce processing and payment
delays, AtestMed significantly impacts the duration of disability social benefits and the associated costs.
Our analysis extends from historical data from 2021 to 2023, inflation adjusted using the National Consumer Price Index (INPC), to future forecasts up to 2028. In our model we use variables related to the Mean
Cost Delay, Cost Delay and Mean Value of Initial Salary Payment. They are all related with the Social Security Temporary Disability Benefit. The study delineates INSS cost patterns with and without the AtestMed
programme, introduced in July 2023, using six time series models (Simple, Holt and Holt-Winters Exponential Smoothing, ARMA, ARIMA, and SARIMA) applied to the Mean Delay Cost variable. Our forecasts
for 2024 predict a R$ 5.6 billion saving, increasing to nearly R$ 30 billion over the next five years, thus
highlighting AtestMed’s pivotal role in financial efficiency and operational improvement in social security
management. This methodological framework not only unravels temporal and seasonal expenditure trends
but also enhances strategic decision-making within the social security domain.

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Keywords: AtestMed Programme · Time Series Forecasting · Social Security System · Temporary Disability Benefits · INSS Cost Optimization · Socioeconomic Impact Analysis
Acknowledgements: The authors Renata Alcoforado and Alfredo Egı́dio dos Reis acknowledge funding
from Project CEMAPRE/REM - UIDB/05069/2020, which is supported by FCT/MCTES through national
funds.

REFINING CANCER INSURANCE PRICING: INSIGHTS FROM
SEMI-MARKOV MODELLING
Ayşe Arık1,∗ , Andrew J.G. Cairns1 , Erengul Dodd2 , Angus S. Macdonald1 , Adam Shao3 ,George Streftaris1
1 Department of Actuarial Mathematics and Statistics, Heriot-Watt University, and the Maxwell Institute forMathematical Sciences, UK
2 Mathematical Sciences and S3RI, University of Southampton, Southampton, United Kingdom
3 Biometric Risk Modelling Chapter, SCOR, Singapore

a.arik@hw.ac.uk (∗ corresponding author) a.j.g.cairns@hw.ac.uk, e.dodd@soton.ac.uk,
a.s.macdonald@hw.ac.uk, ashao@scor.com, g.streftaris@hw.ac.uk
Breast cancer stands as not only one of the most prevalent cancers diagnosed and a leading cause of deathamong women but also ranks among the most common causes of critical illness insurance claims. In thisstudy we focus on pricing of a specialised critical illness and life insurance contract tailored for breast cancer
risk. We compare (a) an industry-based Markov model with (b) a recently developed semi-Markov model,
and an alternative model based on (b). We calibrate all models by using population data in England and datafrom the medical literature. We quantify actuarial net premiums of specialised insurance contracts undervarious scenarios relating to cancer diagnosis and treatment. As part of our modelling, we also estimate
breast cancer survival by age-at-diagnosis and clinical stage. Our analysis shows that the semi-Markov
model leads to results aligned with empirical evidence. Our findings point out the importance of accounting
for the time spent with diagnosed or undiagnosed pre-metastatic breast cancer in actuarial applications.

References[1] Arık A, Cairns AJG, Dodd E, Macdonald AS, Shao A, Streftaris G (2024) The effect of the COVID-19
health disruptions on breast cancer mortality for older women: A semi-Markov modelling approach.
Scandinavian Actuarial Journal, in press.
[2] Arık A, Cairns AJG, Dodd E, Macdonald AS, Shao A, Streftaris G (2023) Insurance pricing for breast
cancer under different multiple state models. https://arxiv.org/abs/2311.15975

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A POISSON-TWEEDIE COLLECTIVE RESERVING MODEL FOR
ESTIMATING PROVIDER GAIN-SHARING PAYMENTS
Ian Duncan1,∗ , Sooie-Hoe Loke2 , Gareth W. Peters1
1 University of California Santa Barbara
2 University of Western Washington

iduncan@ucsb.edu (∗ corresponding author)
Value-based Contracting (VBC) has become a force in the United States healthcare system over the past
decade. Value-based Contracts transfer the risk for patient financial outcomes from the insurance payer toproviders. The Centers for Medicare and Medicaid Services (CMS) expects 100% of all Medicare providers
to be in a VBC contract by 2030. Different forms of VBC exist; a prevalent type of contract between insurer
and medical provider is “gain-sharing.” Under a gain-sharing contract a target cost for an insured population
is established in advance of the contract period; if the population cost at the end of the period is less thantarget, a gain occurs that is shared between the insurer and provider (the converse occurs when the result
is a loss). One consequence of providers taking gain-sharing risk is that the reconciliation of final amounts
owing does not take place until at least 18 months (or later) after the start of a contract year because of theneed for a year’s experience plus claims run-out. If the provider is owed gains, the actual amount would not
be received for at least 6 months after the close of the contract year. Negotiation of the final settlement adds
months, with payments often delayed until 24 months after the inception of the contract. Conversely, the if
the provider owes a reimbursement to the payer the same delay occurs in payment. In either case both parties
will have to establish a reserve for an estimated payment on its balance sheet. Given the uncertainty inherent
in the ultimate reconciliation the balance sheet provision will likely be conservative unless the provider hasa means of reasonably estimating the ultimate gain or loss.
There are some solutions that are implemented in practice:
1. Providers receive fee-for-service payments until the target budget is exhausted, which implies that
there is neither a gain to the providers nor (in a two-sided contract) a reimbursement due the payer.
At this point no further payments are made to providers. This model is clearly sub-optimal for bothparties. This solution favors the first-mover advantage and providers that attempt to extract payment
late in a contract year could lose reimbursement. It also does not address the amount or timing of thepotential final payment.
2. Payments are made subject to a hold-back percentage that attempts to mirror the amount that aprovider would receive under a no-gain/no-loss contract. For example, assuming the application of ahold-back discount factor of 5%, providers would be paid 95% of their submitted claims. While allproviders are then paid a portion of submitted claims, this method suffers from the problem that theamount of submitted claims could exceed the pre-specified target despite the discount. In this casethe providers end the year with amounts owing to the payer and will need to hold reserves on theirbalance sheet.
3. Recently the idea of “interim” reconciliations has been gaining in popularity. Under this model interim
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settlements take place and funds are either released or re-captured based on the interim reconciliation.
While this model is likely more accurate than either of the previous two models, the reconciliation
could be inaccurate resulting in in over- or under-payments. The problem of reserving for the ultimate
payment would be readily soluble should the payer know or reasonably estimate the ultimate outcome.
We propose a statistically-based payment model where instead of paying a lump sum at the end of
the 18-month period (after knowing the actual amounts of all claims), the providers receive monthly,varying amounts which are constantly re-evaluated as new claims are submitted for payment and thepayer’s estimated reserve is updated as well.
In this paper we adapt the Collective Risk model for the context of the VBC reserving framework. We
implement our model using a large database of US employer claims data.

Reinsurance
REINSURANCE WITH NEURAL NETWORKS
Aleksandar Arandjelović1,∗ , Julia Eisenberg2
1 Vienna University of Economics and Business, Institute for Statistics and Mathematics, Austria
2 TU Wien, Institute of Statistics and Mathematical Methods in Economics, Austria

aleksandar.arandjelovic@wu.ac.at (∗ corresponding author), julia.eisenberg@tuwien.ac.at
We consider an insurance company who faces financial risk in form of insurance claims and random marketdependent income fluctuations. The company aims to simultaneously control it’s terminal wealth (e.g. at theend of an accounting period) and minimal available capital during this period by purchasing reinsurance.
The multidimensional target functional consists of a utility function penalised by an extended version of a
Gerber–Shiu function. The optimal reinsurance policy, maximizing the target functional, is parametrized via
neural networks. The procedure is illustrated by a numerical example, where the surplus process is given bya Cramér–Lundberg model perturbed by a mean-reverting Ornstein–Uhlenbeck process.
Keywords: Optimal control · Reinsurance · Deep learning · Cramér-Lundberg model · Perturbed risk process · Gerber–Shiu penalty function · Ruin probability · Binary classification · Pareto front

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REINSURANCE PRICE AS A TWO-STATE MARKOV JUMP PROCESS:HOW TO FIND THE OPTIMAL STRATEGY
Julia Eisenberg1,∗ , Lukas Fabrykowski1 , Maren Schmeck2
1 TU Wien
2 University of Bielefeld

jeisenbe@fam.tuwien.ac.at (∗ corresponding author)
We consider a company who models its surplus by a Brownian motion with drift. The company is allowed
to buy proportional reinsurance in order to reduce the risk. The economy is assumed to evolve in businesscycles (modelled by a 2-state Markov jump process), impacting only the reinsurance price. We seek to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections
needed to prevent writing red numbers. The constant ”once and forever” strategies, optimal for the case of
only one state, turn out to be suboptimal. We develop a recursive approach that allows us to determine theoptimal reinsurance strategies in dependence on the current business cycle.

OPTIMAL REINSURANCE TO MINIMIZE THE PROBABILITY OF
PARISIAN RUIN WITH EXPONENTIAL GRACE PERIOD
Phuong Nguyen1 *, Manuel Guerra1
1 ISEG - Lisbon School of Economics and Management, CEMAPRE

l53645@phd.iseg.ulisboa.pt (*corresponding author), mguerra@iseg.ulisboa.pt
Insurance business involves an exchange of risk for premium income. Insurance company receives premiumin advance and pay a claim when it occurs. Since the claim is random in both time and amount, insurancecompany has to manage its reserve to survive.
Ruin is an insolvency event defined when the reserve of an insurance company fall below a certain
level. However, the insurance company may have many business lines, when one line has problems, it
may get support from other lines so the business does not cease immediately [1]. Also, in many countries
the regulator allows the company to file for a re-organization instead of a bankruptcy process, for example
chapter 11 under US law. Thus, the insurance company is often given some time or grace period, to sort
its finances and avoid ruin. For such reasons, and inspiration from Parisian barrier option in mathematicalfinance, the term Parisian ruin was coined [2]. Parisian ruin allows the company’s reserve to stay below thecritical threshold for a grace period which can be a fixed constant, a function of reserve deficit or a randomvariable with given distribution.
The collapse of an insurance company may affect the economy as a whole, so the insurance company’s
Parisian ruin probability receives concerns from regulators, investors and the insurance company. To manage
the probability of Parisian ruin, the insurance company can use many tools to manage its reserve process like101European Actuarial Journal Conference 2024
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premium pricing, investment, reinsurance. In this study, we will find the probability of Parisian ruin whengrace period is exponentially distributed and the optimal reinsurance treaty to minimize the probability ofParisian ruin from the cedent’s point of view.
Acknowledgements: The first author acknowledges support from FCT–The Foundation for Science andTechnology, Portugal through grant UI/BD/152308/2021. Both authors acknowledge support from FCT
through grant UIDB/05069/2020.

References[1] dos Reis AE (1993) How long is the surplus below zero. Insurance Math. Econom. 12:23–38.
[2] Dassios EA, Wu S (2008) Parisian ruin with exponential claims. LSE Research Online.

OPTIMAL RISK DIVERSIFICATION FOR A REINSURANCE COMPANY
UNDER A STOCHASTIC CLAIM APPROACH
Ozenc Murat Mert1,2,∗ , Ralf Korn1 , A. Sevtap Selçuk-Kestel2
1 Financial Mathematics Group, Department of Mathematics, Rheinland-Palatinate Technical University
2 Department of Financial Mathematics, Institute of Applied Mathematics, Middle East Technical

University
mmert@metu.edu.tr (∗ corresponding author), m.oezenc@rptu.de, korn@mathematik.uni-kl.de,skestel@metu.edu.tr
Given the critical role insurance markets play in the global economy, the necessity for reinsurance contracts
has increased due to factors like population expansion, catastrophic incidents, and political and economic
uncertainties. For instance, the extensive devastation caused by natural disasters such as the Maraş earthquake disaster in Türkiye may surpass the coverage capacity of insurance companies alone. This underscores
the significance of reinsurance policies, particularly in the face of natural disasters such as this. With thesurge in the risk of insurance losses resulting from such events, individual reinsurance firms may decide toenter into agreements with multiple insurance companies. Among these agreements, some are recognized
as stop-loss contracts. This study aims to explore both (i) contracts with retention and (ii) contracts encompassing both retention and upper-limits (cap), which are types of stop-loss contracts. The study focuses on
optimizing risk diversification strategies for reinsurance companies across both types of contracts.
The stochastic loss and exposure curve models to be used in the study are among the factors that increase
the importance of the research in terms of providing both randomness and time-dependent modeling, andmaking a fair premium allocation between the parties. This study is motivated by the studies [1], [2], and[3], in which the geometric Brownian motion model and Pareto-Beta jump diffusion model are used in loss
modeling and the examination of loss under GBM in terms of drift and diffusion and the examination of loss
under Pareto-Beta jump diffusion in terms of drift and diffusion, and the jump tendency that is caused byextreme-valued losses resulting from events such as natural disasters are aimed.
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In this study, we consider the stop-loss contracts involving one reinsurer and two insurers under thestochastic claim approach. For this, we propose the Heston model with approximated variance process tocapture the dynamics of the sum of claim amounts belonging to different stop-loss contracts. Under thisassumption, we implement the time-influence on stop-loss contract in the frame of the stochastic model andderive the parties’ time-dependent expected costs and exposure curves. Moreover, the analytical expressionsof exposure curves are presented to ascertain the allocation of premiums between the reinsurer and insurer,
considering factors such as time, loss, retention, and both retention and cap mechanisms.
Furthermore, in this study, we use partially real data due to difficulties such as confidentiality in accessing real data in terms of actuarial losses. The other part of the data to be used is obtained through simulation
on real data and we examine the compatibility of the proposed model with this data. In this regard, parameter
estimates and error analyzes are made under some analytically derived assumptions.
The main aim of the study is to find the optimal risk diversification levels of for the stop-loss contracts
with one reinsurer and two insurers for both contract types and to represent them as barrier levels which
are derived from the equivalence relationship between the expected total costs of the reinsurer and insurers.
To achieve this, we formulate the analytical expression for the total cost difference. Obtaining a solution
in closed form poses challenges due to the integration of characteristic functions from the Heston model,
resulting in complex numbers. Hence, we employ the Newton iteration with an adaptable learning rate tofind the optimal barrier levels. We also give numerical illustrations for our findings and we anticipate thatthe findings of this study will provide practical insights for practitioners in devising strategies that involve
multiple stop-loss contracts and optimizing premium allocation within their optimal framework.
Acknowledgement: Ozenc Murat Mert was supported from the 2219 International Postdoctoral Research
Fellowship Program, under grant number 105B192300266, of the Scientific and Technological Council ofTürkiye (TUBITAK).

References[1] Mert OM, Selcuk-Kestel S (2022) Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics 51(1):288–307.
[2] Mert OM, Selcuk-Kestel S (2021) Time dependent stop-loss reinsurance and exposure curves. Journalof Computational and Applied Mathematics 389:113348.
[3] Mert OM (2022) Stochastic Modeling of Stop-Loss Reinsurance and Expsoure Curves Under Time
Dependent Structure. Ph.D. - Doctoral Program, Middle East Technical University.

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WEDNESDAY, SEPTEMBER 11th
PLENARY SESSION III
CONFRONTING EMERGING RISKS WITH FLEXIBLE GENERALMODELS; A FOCUS ON CYBER RISKMarie Kratz1
1 ESSEC Business School

kratz@essec.edu
Addressing emerging risks such as aging, climate change, and cyber threats poses significant challenges
for societal actors. (Re)insurance companies play a crucial role in mitigating these risks by enhancing
resilience through prevention, response, and recovery measures. Simultaneously, these challenges present
business opportunities. Consequently, extensive research has been undertaken to better understand theserisks and develop appropriate models using tools from probability, (computational) statistics, time series
analysis, and machine learning. Focusing on cyber risk, we propose a general yet straightforward model that
automatically fits both the body and tail behaviors of the empirical loss distribution. This risk model canbe applied to risk management, enabling the quantification of a (re)insurance company’s liabilities throughmathematical expectation (essential for calculating the risk premium) and capital through risk measures.
Additionally, our method addresses the practical issue of evaluating the tail distribution by automaticallydetecting the threshold for extreme observations, without resorting to computationally intensive methods.
This improves upon standard Extreme Value Theory (EVT) methods that necessitate separate treatment for
the tail, or other dynamic EVT approaches that rely on arbitrarily high thresholds. Particularly, it enhances
efficiency in Extreme Value Regression, revealing the factors influencing the likelihood of extreme events.

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PARALLEL SESSIONS VI
Climate Risks 3
MITIGATING FLOOD RISK WITH CAT BONDS: A NEW ORLEANS CASE
STUDY
Abraham Hernández-Pacheco1,2,∗ , Roberto Carcache Flores1
1 VITALIS, Today for Tomorrow
2 ISEG & CEMAPRE, Universidade de Lisboa

abe@vitalis.com.mx (∗ corresponding author), rcarcache@vitalis.com.mx
Floods cause billions of dollars in losses each year and involve different natural disasters like hurricanes,
mudslides, and prolonged rainfall. Data from the Federal Emergency Management Agency (FEMA) indicates that flood losses in the U.S. have increased in severity and frequency over the years, stemming fromclimate change and a greater number of extreme weather events. This paper presents a case study of how
catastrophe (CAT) bonds can be used to manage the financial risk of flooding in Orleans Parish, an area withhigh exposure to flooding, according to data retrieved from FEMA.
We present a multi-period model for the valuation of a CAT bond with an indemnity trigger, that aims
to provide coverage for extreme flood losses. This valuation method incorporates Extreme Value Theory tomodel flood losses. The price of the CAT bond is obtained through Monte Carlo simulations with stochastic
rates. Different assumptions are then tested, to show the sensitivity of the CAT bond’s price to the coverage
provided and the model parameters.

DESERT DUST STORM INSURABILITY: A PRIMER
Andreas Milidonis1,∗ , Marina Solomou1 , Panayiotis Kouis2 , Petros Mouzourides3 ,Marina Neophytou3
1 Department of Accounting and Finance, School of Economics and Management, University of Cyprus
2 Respiratory Physiology Laboratory, Medical School, University of Cyprus
3 Environmental Fluid Mechanics Laboratory, University of Cyprus

milidonis.andreas@ucy.ac.cy (∗ corresponding author), solomou.marina@ucy.ac.cy
According to the WHO and US Environmental Protection Agency [3], poor ambient air quality subject
to excessive concentrations of particulate matter (PM) is one of the five most severe health risks globally,
along with obesity, diabetes, high blood pressure, and smoking. The global burden of disease related to PM[6] has been well-documented, linking non-accidental daily mortality and morbidity to long-term exposure
to coarse particles P M10 (with aerodynamic diameter < 10µ m). In 2020, air pollution’s global healthimpacts cost was estimated to be $2.3 trillion which translates to the 2.7% of the gross world product [5],105European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024with approximately 4.2 million deaths worldwide being attributed to increased PM exposure.
PM concentrations arise through two types of sources. The former includes anthropogenic activities
such as industrial production, and the latter includes natural sources like Desert Dust Storms (DDS). DDS
are natural hazards occurring around the globe, and have been examined by the environmental engineering
literature over the past several years [1]. However, to the best of our knowledge, there have not been papers
discussing the transfer to DDS hazards to financial markets.
In this paper, we focus on the natural hazard of DDS, and make the case that financial and insurance
instruments can be used to mitigate the adverse socioeconomic effects of DDS through the solidificationof DDS insurability. We start from the DDS definition of [2], that we refine by focusing on independently
measured criteria consistent with the criteria set of prior studies. Using representative data to identify DDS
from rural background stations in Southern Europe, we test the impact of DDS on mortality, morbidity andthe implied impact on spending habits within the economy [1].
According to [2] about 18% of the days within a year are impacted by a DDS event. Using datasets fordaily deaths and hospital admissions from Eastern Europe (2006-2017), and following the epidemiologicalliterature, we test whether daily death counts and hospital admissions are abnormally higher on days affectedby DDS (henceforth “DDS days”). We document an increase in both the number of daily deaths and hospital
admissions on DDS days of the order of 3.5% and 5.5%, respectively.
We next focus on “Severe DDS days” to test whether the adverse effects on human mortality and morbidity amplify, subject to the daily P M10 concentration averages. “Severe DDS days” are classified as thedays with average P M10 concentration levels greater than 160 µg/cm3 , denoting a subset of the initial DDS
days sample and the remaining DDS days are classified as “ Mild DDS days”. As expected, severe DDS
days occur less frequently, solidifying the case for insurability. We show that the impact of severe DDS days
on daily deaths increases from ≈ 3.5% to ≈ 20% and from ≈ 5.5% to ≈ 6.4% for daily hospitalizations.
Moving forward we propose an insurance mechanism to mitigate the financial impact from the documented increase in mortality risk on DDS days and the even larger increase in mortality documented on
severe DDS days. Such a contract can be written between a sovereign in Southern Europe 1 to mitigate themonetary loss from premature loss of life and the increased number of hospital admissions. A comprehensive approach is employed for the construction of the insurance contract, based on a fixed benefit payment(as a function of the statistical value of life), that is triggered on DDS days or on severe DDS days. For
the mitigation of the risk exposure of smaller organizations, corporations and/or other entities we further
propose a Dust Index Futures (DIF) that can be used as a way to hedge the DDS induced risk on the cash
flows of certain industries oppositely affected from DDS. DIF can be written in a similar manner to other
weather derivatives traded at the CME (Chicago Mercantile Exchange) such as temperature index futures.
Finally, to insure against a potential catastrophic event, such as ≈ 600 µg/cm3 denoting the maximum
P M10 concentration in our sample, 12 times greater than the European air quality standards, a DDS CAT
bond could be used, similar to the structure of CAT bonds for catastrophe risk in the US. Such an instrument
can offer capital to insurance firms if such events materialize, providing to investors additional diversification
opportunities. Our results have public policy implications. Given that the adverse DDS on human mortality
and morbidity can be treated as an insurable risk, the underlined discussion can be extended in insurance
1
In its efforts to mitigate the adverse effects arising from natural hazards to the society and the economy, this contract could be
written by The European Union itself. DDS could be one of many natural hazards that the EU could insure against, where otherexamples could include earthquakes, floods, draughts, wildfires, landslides etc.

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board rooms or policy makers’ agendas, facilitating the potential of greater risk mitigation.

References[1] Achilleos S, Evans JS, Yiallouros PK, Kleanthous S, Schwartz J, Koutrakis P (2014) Pm10 concentration levels at an urban and background site in Cyprus: the impact of urban sources and dust storms.
Journal of the Air & Waste Management Association 64(12):1352–1360.
[2] Achilleos S, Mouzourides P, Kalivitis N, Katra I, Kloog I, Kouis P, et al. (2020) Spatio-temporalvariability of desert dust storms in eastern Mediterranean (Crete, Cyprus, Israel) between 2006 and2017 using a uniform methodology. Science of the Total Environment 714:136693.
[3] Cohen AJ, Brauer M, Burnett R, Anderson HR, Frostad J, Estep K, Balakrishnan K, Brunekreef B,
Dandona L, Dandona R, Feigin V (2017) Estimates and 25-year trends of the global burden of disease
attributable to ambient air pollution: an analysis of data from the Global Burden of Diseases Study
2015. The Lancet 389(10082):1907–1918.
[4] Liu C, Chen R, Sera F, Vicedo-Cabrera AM, Guo Y, Tong S, et al. (2019) Ambient particulate air
pollution and daily mortality in 652 cities. New England Journal of Medicine 381(8):705–715.
[5] Romanello M, McGushin A, Di Napoli C, Drummond P, Hughes N, Jamart L, et al. (2021) The 2021
report of the lancet countdown on health and climate change: code red for a healthy future. The Lancet
398(10311):1619–1662.
[6] World Health Organization (2021) WHO global air quality guidelines: particulate matter (PM2.5 andP M10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide. World Health Organization.

DISCRETE MULTIVARIATE GENERALIZED PARETO DISTRIBUTION
WITH APPLICATION TO THE STUDY OF DROUGHTSSamira Aka1,2,∗ , Marie Kratz1 , Philippe Naveau2
1 ESSEC Business School, CREAR, Cergy-Pontoise, France
2 IPSL & Université Paris Saclay, Gif-sur-Yvette, France

samira.aka@ens.uvsq.fr (∗ corresponding author), kratz@essec.edu, Philippe.Naveau@lsce.ipsl.fr
In the insurance industry, addressing discrete extreme events, such as the number of fires or insurance
claims, is crucial for risk management and policy planning. Modeling these occurrences, especially when
considering multiple variables or geographic locations, is challenging but essential. Understanding thesepatterns helps insurers set appropriate premiums and develop effective strategies to mitigate risks associatedwith droughts and other natural disasters.
Relying on the existing theory for the Generalized Pareto Distribution ([1, 2]), this presentation explores
some extensions of multivariate Extreme Value Theory (EVT) to discrete settings.
The main objective of our study is to widen knowledge on the representation of discrete extreme count107

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data, especially discrete exceedances over thresholds with Multivariate Discrete Generalized Pareto distributions (MDGPD).
Through theoretical results and illustrative examples, this presentation outlines the construction andproperties of the Multivariate Discrete Generalized Pareto Distribution (MDGPD). Additionally, it provides
practical insights into simulation techniques and data fitting approaches for MDGPDs. The proposed framework expands the toolkit for modeling extreme events, offering a methodology for analyzing multivariate
discrete data with extreme values. Given the growing concern about droughts for insurers in Europe, anapplication of this method to drought analysis will be presented.

References[1] Hitz A, Davis R, Samorodnitsky G (2024) Discrete extremes. Journal of Data Science 1–13.
[2] Rootzén H, Segers J, Wadsworth JL (2018) Multivariate generalized Pareto distributions: Parametrizations, representations, and properties. Journal of Multivariate Analysis 165:117–131.

A CAUSAL MACHINE LEARNING APPROACH FOR ESTIMATINGHETEROGENEOUS TREATMENT EFFECTS IN THE PRIMARYCATASTROPHE BOND MARKET
Despoina Makariou1,∗ , Pauline Barrieu2 , Yining Chen2
1 University of St Gallen
2 London School of Economics and Political Sciencedespoina.makariou@unisg.ch(∗ corresponding author), P.M.Barrieu@lse.ac.uk, Y.Chen101@lse.ac.uk
In this paper, we study the market timing in the insurance linked security sector. The focus naturally lies on
the catastrophe bond market which is the most prevalent subset of the insurance linked security domain. In
particular, we aim to estimate the causal effect of catastrophe bond issuance timing on their spreads whileaccounting that the causal effect may vary for different subgroups of catastrophe bonds in our population but
without pre-specifying how. Studying the issuance timing is important because it can directly impact the costof catastrophe risk transfer for the issuer and the attractiveness of the bond as an investment opportunity forthe investor. Our methodology involves estimating the heterogeneous treatment effects in a non-parametricmanner utilising a machine learning technique called causal forest, see [2]. The aforementioned method
extends the traditional random forest algorithm of [3] which was found to be successful in solving prediction
problems in various sectors including in a catastrophe bond setting, see [1]. However, unlike random forest
which is geared towards solving prediction problems, causal forest provides a flexible and interpretable
framework for causal inference and estimation of heterogeneous treatment effects in observational studies
and randomised experiments. The reason behind choosing a non-parametric approach for the heterogeneous
effects estimation is to account for interactions and non-linear patterns between the explanatory variables
and the response without having to explicitly define them and also to be able to discover potentially potent
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but unexpected treatment effect heterogeneity. We find that issuing a catastrophe bond in the first part ofa calendar year is associated to a lower spread and this result varies according to factors such as market
conditions and other issuance characteristics.

References[1] Makariou D, Barrieu P, Chen Y (2021) A random forest based approach for predicting spreads in the
primary catastrophe bond market. Insurance: Mathematics and Economics 101:140–162.
[2] Athey S, Tibshirani J, Wager S (2019) Generalized random forests. The Annals of Statistics
47(2):1148–1178.
[3] Breiman L (2001) Random forests. Machine learning 45:5–32.

Mathematical Finance 3
A SUSTAINABLE APPROACH TO RETIREMENT INVESTING FOR THE
LONG HAULJean René Mwizere1,∗ , Iqbal Owadally1 , Andrew Clare1
1 Bayes Business School, London

jean-rene.mwizere@bayes.city.ac.uk (∗ corresponding author), m.i.owadally@city.ac.uk,
a.clare@city.ac.uk
This paper delves into the performance evaluation of funds with portfolios adhering to sustainable investment criteria compared to conventional index tracker funds. To present empirical results, we introduce aseries of investment approaches based on combining stock market capitalization and ESG scores for portfolio weighting. Furthermore, we incorporate asset allocation strategies and glide paths currently utilized bymaster trust funds in the United Kingdom. This research aims to assess the impact of environmental, social,and governance (ESG) considerations on long-term retirement plans while showcasing the potential for retail investors to manage their investment schemes passively. Through comprehensive analysis, our findings
demonstrate that all four examined investment approaches outperform a standard index tracker portfolio interms of pension accumulation and overall financial performance. This substantiates the potential benefitsof integrating sustainable investment principles into portfolio management strategies. Moreover, our paper
uncovers a statistically significant difference in performance between ESG-screened portfolios and funds
that do not prioritize adherence to sustainability criteria. This emphasizes the prospective importance ofconsidering ESG criteria while undertaking investment decisions, as they can have a tangible impact on
portfolio outcomes.
Keywords: Environmental, social and governance (ESG) · Sustainable investment · Socially responsible
investment (SRI) · Glide path, and shorting109

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TERM STRUCTURE SHAPES IN THE SVENSSON FAMILY
Martin Keller-Ressel1,∗ , Felix Sachse1
1 Institute for Mathematical Stochastics, TU Dresden, 01062 Dresden, Germany

martin.keller-ressel@tu-dresden.de (∗ corresponding author), felix.sachse@tu-dresden.de
The Nelson-Siegel family [3] x β x
2
β0 + β1 exp −+ x exp −,τττ
and the Svensson family [4]xβ0 + β1 exp −
τ1







β2
x
β3
x
+ x exp −+ x exp −
τ1
τ1
τ2
τ2

are used by European central banks to model the forward curve [1]. In the literature on term structure
modeling one can, more or less frequently, find mentions of attainable shapes of these forward curves ortheir corresponding yield curves. For example, Nelson and Siegel mention that their yield curves obtainmonotonic, humped and S shapes; and in [1] it is claimed that Svensson curves can attain two humps. Bothclaims are indeed correct but, although it is relatively easy to determine attainable shapes of Nelson-Siegel
curves, for both claims we could not find any proof in the literature.
In this paper we use a geometric approach from [2] to partition the parameter spaces into regions corresponding to identical shapes and show that the curves from the Nelson-Siegel family can attain all shapeswith at most one local extremum and in the Svensson family all shapes with at most 3 local extrema are
attainable. This also holds for the corresponding yield curves.
We apply our results to the Svensson-consistent Heath-Jarrow-Morton model, obtaining insight aboutattainable term structure shapes, possible transitions between them and the relative frequency of different
shapes. We do this for both the forward curve and the yield curve.
We analyze yield curve data provided by the ECB and find that, at least in terms of attainable term
structure shapes, a more parsimonious model than the Svensson family might be more appropriate to use.

References[1] BIS (2005) Zero-coupon yield curves: Technical documentation. BIS papers, (25).
[2] Keller-Ressel M, Sachse F (2023) State space decomposition and classification of term structure shapes
in the two-factor Vasicek model. International Journal of Theoretical and Applied Finance 2350013.
[3] Nelson CR, Siegel AF (1987) Parsimonious modeling of yield curves. Journal of business 60(4):473–
489.
[4] Svensson LEO (1994) Estimating and interpreting forward interest rates: Sweden 1992-1994. NBER
Working Paper Series 4871.

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AFFINE VALUATION OF VARIABLE ANNUITIESDavid Criens1 , Raquel Gaspar2 , Thorsten Schmidt1∗
1 University of Freiburg, Germany
2 ISEG, Lisbon, Portugal

david.criens@stochastik.uni-freiburg.de, rmgaspar@iseg.ulisboa.pt,
thorsten.schmidt@stochastik.uni-freiburg.de (∗ corresponding author)
Abstract
In this paper we introduce and affine setting for a financial market and related insurance quantities.
Assuming no insurance-finance arbitrage (NIFA), we derive valuation formulas for variable annuities
and similar products. This general framework includes dependencies of mortality and stock markets, as
recently observed during the corona pandemic. In addition, surrender may also depend on the driving
affine process and, hence, on the stock market.

Motivation
The fair valuation of cash flows is an important problem in insurance mathematics. The valuation of
future cash flows is immediately linked to financial markets, as discounting introduces a dependency oninterest rate markets. Some contracts, like variable annuities, even depend explicitly on the financial market
since the pay-off of the contract depends on future values of indices or stock prices.
For complete financial markets, the classical valuation rule may be based on the risk-neutral valuation
principle, i.e., prices are computed as discounted expectations with respect to the (unique) risk-neutral
pricing measure, the so-called equivalent martingale measure (EMM). In a similar way, the valuation of
insurance products based on sufficiently large insurance pools is based on the law of large numbers andpremiums are computed via a discounted expectations under the real-world measure.
When considering hybrid products, products depending explicitly on financial components, one needs
to proceed more carefully. Examples of hybrid products are unit-linked insurance contracts, various catastrophe futures and options, financial stop-loss reinsurance contracts and variable annuities. The valuation ofthese products is a major challenge and several different (multi-step) valuation rules have been suggested in
the literature.
Insurance–Finance Arbitrage
Many of these valuation rules are justified by splitting the product into hedgeable and unhedgeable partsfor which different pricing operations are suggested. A novel approach to derive a pricing rule for hybrid
products has been suggested by Artzner et al. in the recent paper [1]. Instead of using an hedgeability
argument, Artzner et al. study the problem from a no arbitrage perspective. Namely, they introduce a concept of insurance–finance–arbitrage (IFA) and prove a corresponding fundamental theorem of asset pricing,i.e., the equivalence of the absence of IFA and the existence of an insurance–finance martingale measure(IFMM). The main hypothesis in the framework from [1] is that insurance companies have large enoughpolicy portfolios with conditionally i.i.d. claims, which allow, from a technical point of view, an applicationof the (conditional) law of large numbers.

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A prominent rule which can be used for the valuation is the so-called QP–rule. Formally, the QP–rulecomputes the price of a hybrid option by first taking a conditional P -expectation and then a conditional expectation w.r.t. some EMM. In other words, the rule combines the classical valuation principles for financial
and insurance contracts. Under reasonable assumptions, the QP–rule is insurance–finance consistent, i.e.,
it is shown to be a (conditional) expectation w.r.t. an IFMM. In other words, it corresponds to a classicalpricing rule from a financial point of view.
The goal of this paper to show the feasibility of the QP-rule in a rich class of models. For its particular
suitability for modelling dynamic mortality rates and financial markets we chose the framework of affine
processes as a starting point.
Affine processes
Affine processes are a highly tractable class of processes and very suited to the question at hand, inparticular for modeling stochastic mortality term structures. In this paper we propose a new framework indiscrete time for the valuation of insurance products linked to financial markets. This generalizes existing
approaches in three aspects: first, we incorporate the QP-approach in a general setting with allows for
dependencies between financial markets, mortality, surrender and further factors. Note that this requires
modelling the affine process under P for the insurance quantities and under Q for the parts of the affine
process referring to the financial market.
Second, it is important to acknowledge that the insurance part of the contract is monitored in discretetime, however. We therefore consider a discrete affine framework, i.e. an affine process with stochastic discontinuities. In the existing works in the insurance literature, only stochastically continuous affine processes
are used. Third, we introduce new valuation formulas for more than one stopping time, to include stochastic mortality and surrender, for example. We show explicitly how to value a variable annuity and similar
products in this framework.

References[1] Artzner P, Eisele K-T, Schmidt T (2024). Insurance–finance arbitrage. Mathematical Finance.

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ENHANCING VALUATION OF VARIABLE ANNUITIES IN LÉVY MODELS
WITH STOCHASTIC INTEREST RATES
Ludovic Goudenege1 , Andrea Molent2 , Antonino Zanette2,∗ , Xiao Wei3
1 Féderation de Mathématiques de CentraleSupélec - CNRS FR3487, France
2 Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Italy
3 China Institute for Actuarial Science, School of Insurance, Central University of Finance and Economics,

Chinaantonino.zanette@uniud.it (∗ corresponding author), ludovic.goudenege@math.cnrs.fr,
andrea.molent@uniud.it, weixiao@cufe.edu.cn
This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed
minimum benefits under a Lévy equity market by considering a stochastic interest rate described by the HullWhite model. This framework allows for a realistic and dynamic financial environment. We provide a robust
valuation mechanism based on a hybrid numerical method which combines tree methods for interest ratewith finite difference for the underlying asset price. This method is particularly suited for the complex natureof variable annuities where periodic fees and mortality risks are significant considerations. Our findings
reveal the impact of stochastic interest rates on the strategic decision-making process related to the surrenderof these financial instruments. Through extensive numerical experiments, and using comparison against
Longstaff-Schwartz Monte Carlo method, we demonstrate how our enhanced model can guide policyholders
and issuers in structuring contracts that balance the interests of both parties, particularly in disincentivizing
premature surrender while accommodating the realistic fluctuations of the financial markets. Finally, acomparative analysis with varying interest rate parameters highlights the impact of the interest rate on thecost of the optimal surrender strategy and highlights the relevance of proper modelling for the stochastic
interest rate.

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Statistical Methods 2
PREDICTION INTERVALS FOR PARETO RECORD CLAIMS –COMPARISONS AND APPLICATIONS
Christina Empacher1 , Udo Kamps1,∗ , Anja Bettina Schmiedt2
1 Institute of Statistics, RWTH Aachen University, Aachen, 52056, Germany
2 Department of Mathematics, Rosenheim Technical University of Applied Sciences, 83024 Rosenheim,

Germany / Actuary DAV
udo.kamps@rwth-aachen.de (∗ corresponding author),
christina.empacher@rwth-aachen.de, anja.schmiedt@th-rosenheim.de
Statistical modelling with record values and respective statistical inference are of interest in various fields.
Basic references on record values are [1] and [7]. Based on record values in a sequence of iid randomvariables, several authors study point and interval prediction of future record values (see, e.g., [2] - [4],[6], [8] - [11]). In actuarial science, prediction and evaluation of extreme claims or losses are fundamental
for pricing and quantitative risk assessment. Respective methods from extreme value analysis are wellestablished and, e.g., may lead to long-term prediction via high quantiles. Here, the problem of predicting afuture record claim is addressed by means of prediction intervals based on a sequence of previously observed
record claims. The study and prediction of record values is understood as a supplementing and decisionsupporting tool in risk analysis and internal risk assessment. Former results on exact and approximate
prediction intervals for future upper record values from an underlying Pareto distribution are summarized
and modified and new ones are contributed based on a maximum-product-of-spacings predictor (see [11]).
In a simulation study, these prediction intervals are evaluated and compared regarding coverage frequency
and length. Selected prediction methods are applied to several real data sets from the insurance industry,
which turn out to perform well. The use of the Pareto distribution is discussed along with the common
situation of a fairly small number of observed record values. The methods seem to be able to capture themagnitude of future record claims, even for small numbers of record observations (cf. [5]). Moreover, an
outlook on point and interval prediction with an underlying generalized Pareto distribution is given.
Keywords: Record values · Interval prediction · Pareto distribution · Generalized Pareto distribution · Insurance data sets

References[1] Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York.
[2] Asgharzadeh A, Abdi M, Kus C (2011) Interval estimation for the two-parameter Pareto distribution
based on record values. Selcuk J. Appl. Math. 149–161.
[3] Awad AM, Raqab MZ (2000) Prediction intervals for the future record values from exponential distribution: comparative study. J. Stat. Comput. Simul. 65:325–340.

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[4] Basak P, Balakrishnan N (2003) Maximum likelihood prediction of future record statistics. In: Mathematical and Statistical Methods in Reliability, eds.: B Lindqvist, K Doksum. World Scientific Publishing, New York, 159–175.
[5] Empacher C, Kamps U, Schmiedt AB (2024) Prediction intervals for future Pareto record claims.
Submitted.
[6] Empacher C, Kamps U, Volovskiy G (2023) Statistical prediction of future sports records based onrecord values. Stats 6:131–147.
[7] Nevzorov VB (2001) Records: Mathematical Theory. American Mathematical Society, Providence.
[8] Raqab MZ (2007) Exponential distribution records: different methods of prediction. In: Recent Developments in Ordered Random Variables, eds.: M Ahsanullah, MZ Raqab. Nova Science Publishers,
Hauppauge, 239–251.
[9] Raqab MZ, Ahmadi J, Doostparast M (2007) Statistical inference based on record data from Paretomodel. Statistics 41:105–118.
[10] Volovskiy G, Kamps U (2020) Maximum observed likelihood prediction of future record values. TEST
29:1072–1097.
[11] Volovskiy G, Kamps U (2020) Maximum product of spacings prediction of future record values.
Metrika 83:853–868.

APPROXIMATION OF ABSOLUTELY CONTINUOUS RANDOMVARIABLES FOR THE ASSESSMENT OF THE DISTRIBUTION OFCOMPOUND SUMS
Alessandro Barbiero1,∗ , Asmerilda Hitaj2
1 Department of Economics, Management and Quantitative Methods, Università degli Studi di Milano
2 Department of Economics, Università degli Studi dell’Insubria

alessandro.barbiero@unimi.it (∗ corresponding author), asmerilda.hitaj@uninsubria.it
The accurate evaluation of the distribution of a compound sum is a crucial task in actuarial science and operational risk management. For non-life insurance companies, the total claims amount over a specific period
can be represented as SN = X1 + ... + XN , where N denotes the number of occurring claims and Xi thei-th claim size (i = 1, ..., N ); we assume that the Xi ’s are iid positive random variables, typically continuous, and N is a counting random variable independent of the Xi ’s. The exact evaluation of the distributionof SN is analytically challenging and computationally demanding, if addressed numerically. One common
approach is to approximate it using normal, normal-power or translated Gamma distributions, whose parameters values are obtained by matching the same-order moments. Alternatively, a recursive approach for thedetermination of the distribution of SN is available (Panjer’s formula), which can be used when the claim
size is discrete and the claim frequency distribution belongs to the (a, b, 0) class [1, chapter 9]. In our study,
we propose different discretizations of the continuous claim size over a lattice, in addition to the standard
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technique that preserves the original survival function over the lattice values. These discretizations are basedon the minimization of a discrepancy measure between distribution functions [2]. We compare their performance in recovering the distribution of SN using Panjer’s formula - also in terms of the discretization span with that of other available methods. Additionally, an approximation of the aggregate claims distribution
by a three-parameter Weibull distribution is assessed. Our analysis considers specific frequency and size
combinations for which the exact distribution of SN is known analytically or can be readily determined
numerically.
Acknowledgements The first author acknowledges support by the PRIN2022 project “The effects of climatechange in the evaluation of financial instruments” financed by the “Ministero dell’Università e della Ricerca”
with grant number 20225PC98R, CUP Code: G53D23001960006.

References[1] Klugman SA, Panjer HH, Willmot GE (2019) Loss models: from data to decisions. John Wiley &Sons. Hoboken, New Jersey.
[2] Barbiero A, Hitaj A (2021) A new method for building a discrete analogue to a continuous randomvariable based on minimization of a distance between distribution functions. In: 2021 International
Conference on Data Analytics for Business and Industry (ICDABI), Sakheer, Bahrain, pp.338–341.

STOCHASTIC ORDERS UNDER UNCERTAINTY
Alfred Müller1
1 Universität Siegenmueller@mathematik.uni-siegen.de
We study stochastic order relations under uncertainty. There is an enormous amount of literature on stochastic order relations as a tool to compare probability distributions under only partial information on the preference relation of the decision maker. There is also a growing literature on robust decisions under uncertainty
when there is only partial knowledge of distributions. However, the combination of these two topics has
hardly been considered in the literature so far. It is shown that we cannot expect any reasonable robustness of classical first order stochastic dominance, whereas such properties hold for some versions of almost
stochastic dominance, as almost stochastic dominance is naturally related to robustness with respect to the
Wasserstein distance. We also review other recent results on almost stochastic dominance under uncertainty
where the uncertainty sets are either described by knowing only mean and variance or by knowing only themarginal distribution in a multivariate context.

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Pensions
INVESTIGATING TRADE-OFFS IN THE DESIGN OF SMOOTH PENSIONPRODUCTS
Philipp C. Hornung1,∗ , Mogens Steffensen1
1 University of Copenhagenpcho@math.ku.dk (∗ corresponding author)
We investigate different ways to design smooth pension products based on solutions from op- timal consumption and investment problems. Smoothness of a consumption process can be studied from both apathwise (measured in terms of quadratic variation) and a pointwise (measured in terms of variance) pointof view and we conclude that introducing one type of smoothing does not necessarily improve the other typeof smoothing. Thus care has to be taken when designing smooth pension products.
Focusing on pathwise smoothness without disregarding pointwise smoothness, we provide both a qualitative as well as a quantitative discussion of the trade-offs involved. In the qualitative discussion we findthat to increase smoothness it is necessary either reduce the starting value, the drift of consumption or thelevel of terminal wealth.
For the quantitative discussion we set up an optimal consumption and investment problem, where the firstcontrol is the proportion of wealth invested into the risky asset, but the second control is not the consumption
process itself. Instead we use the drift and volatility of con- sumption as controls. The objective is tominimise the quadratic distance to a target drift and volatility, while introducing a penalty on the volatility.
We find explicit solutions to this prob- lem using classic dynamic programming methods and use them tostudy the three trade-offs theoretically and numerically.
All three approaches result in both pointwise and pathwise smoothing compared to the target, but reducing the drift yields better pointwise smoothing for similar levels of pathwise smoothing.

TONTINES WITH MONEY-BACK GUARANTEE
Sascha Günther1,∗ , Peter Hieber1
1 Université de Lausanne

sascha.gunther@unil.ch (∗ corresponding author), peter.hieber@unil.ch
Tontines are retirement products in which members pool their capital funds to provide the survivors witha stream of income. They receive a certain part of their annual payments through a share of the funds ofthe deceased members. This way, they share the mortality risk among themselves and do not require an
insurance company to manage the tontine. For more details, see, for example [3], [4].
The first original tontines have been set up as early as in the 17th century. However, their unfamiliarity andlack of guaranteed payments might deter potential customers. Tontines with money-back guarantees provide
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the policyholders (or their descendants) a payoff of at least their initial investment. While they reduce theannual benefits to survivors, they offer a feature that might reduce scepticism towards tontine products. In
contrast to refundable income annuities, the insurance provider does not hold any mortality or financial risk.
We compare their characteristics to other products that combine features of annuities and tontines, such as
tonuities and antines that have been introduced by [1] and [2].

References[1] Chen A, Hieber P, Klein JK (2019) Tonuity: A novel individual-oriented retirement plan. ASTIN
Bulletin: The Journal of the IAA 49(1):5–30.
[2] Chen A, Rach M, Sehner T (2020) On the optimal combination of Annuities and Tontines. ASTIN
Bulletin: The Journal of the IAA 50(1):95–129.
[3] Milevsky MA, Salisbury TS (2015) Optimal retirement income tontines. Insurance: Mathematics andEconomics 64:91–105.
[4] Sabin MJ, (2010) Fair tontine annuity. Available at SSRN 1579932.

TIME-CONSISTENT PENSION POLICY WITH MINIMUM GUARANTEEAND SUSTAINABILITY CONSTRAINT.
Caroline Hillairet1,∗ , Sarah Kaakai2 , Mohamed Mrad3
1 CREST, ENSAE
2 LMM, Le Mans Université
3 LAGA, Université Sorbonne Paris Nordcaroline.hillairet@ensae.fr (∗ corresponding author)
In this talk we propose an adaptive decision criterion for designing an optimal policy that is consistent withboth sustainability and adequacy constraints in pay-as-you-go (PAYG) framework.
Firstly, we introduce a general dynamic framework for modeling a PAYG pension system, with a guaranteed minimum annuitized pension amount. Pensions are financed by the workers’ contribution, and thesocial planner has also the flexibility to invest/borrow from a buffer fund to finance the pension system. The
buffer fund allows the social planner to invest in the financial market. In addition, the reserves accumulated
in the fund allows for demographic (longevity/fertility) shocks to be mitigated over time. An important
challenge is to convey the complexity of the problem, by taking into account key phenomena such as thedemographic risk and its evolution over time, the time and age dependence of agents’ preferences, or financial risks. We adopt a dynamic and continuous time approach, which incorporates the heterogeneity ofoverlapping generations and the non-stationary evolution of the population over time. A similar flexible
population dynamics model is studied in [1], however with deterministic age and time dependent birth andmortality rates, while we consider stochastic demographic rates in our setting. This allows us to take into
account stylized fact of the population dynamics, such as uncertain longevity or dependency ratio increases.
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In particular, the population age composition is not assumed to be stationary, as it often the case. Several
papers in the literature study deterministic models of PAYG pension systems, in which the social planner
can invest in a buffer fund, (see e.g. [4], [1]). However, the buffer fund is assumed to have a known return.
Besides, when the optimal pension policy is derived from optimizing solvency indicators, a sustainability
constraint is only taken into account at an arbitrary terminal time, and there are no adequacy constraints. In
this work, the sustainability of the pension scheme is ensured by imposing a pathwise solvency constraint
on the buffer fund. In addition, we take into account in this work the incompleteness of the financial market,
since it is obviously impossible to hedge perfectly the demographic and economic risks through the financial
market. Thus this extends [3], in which the pension benefit was also a lumpsum at retirement. This meansthat the longevity risk is not taken into account, contrary to our work, since we consider here an adequacy
constraint (minimum pension) directly on the pension amount received by pensioners until their death.
Secondly, we provide new contributions on forward dynamic utilities with stochastic constraints andendowments. Indeed, as the representative of past, present and future generations, the social planner should
aggregate preferences of all pensioners. This aggregation is the key in the fairness criterion as this benevolent social planner aims at dealing with successive overlapping generations fairly. Thus, the social planner’s
decision criterion that appears in the optimization problem’s formulation is composed of the buffer fundutility and an aggregated utility which should capture the heterogeneous preferences of different generations. This motivates the use of forward dynamic utilities to deal with such a complex framework. In
addition, dynamic utilities allow us to propose long-term, time-coherent policies adjusted to the information flow, in non-stationary and uncertain environment. The setting is close to the forward dynamic utilities
of investment and consumption framework in [2], whose results are extended here by considering a given
continuous stream of income (contributions) and stochastic pathwise constraints on the buffer fund (wealth)and pensions (consumption).
To summarize, this talk proposes and investigates an optimal pair investment/pension policy for a PAYG
pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension
amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk
and its evolution over time, the time and age dependence of agents preferences, and financial risks. The
preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic
domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The
preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness
constraints. We design and solve the social planner’s dynamic decision criterion, and compute the optimal
investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities
is provided.

References[1] Alonso-Garcia J, Devolder P (2019) Continuous time model for notional defined contribution pension
schemes: Liquidity and solvency. Insurance: Mathematics and Economics 88:57–76.
[2] El Karoui N, Hillairet C, Mrad M (2018) Consistent utility of investment and consumption. Stochastics
90(6):927–954.
[3] Gabay D, Grasselli M (2012) Fair demographic risk sharing in defined contribution pension systems.
Journal of Economic Dynamics and Control 36(4):657–669.
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[4] Godinez-Olivares H, Boado-Penas C, Haberman S (2016) Optimal strategies for pay-as-you-go pension finance: A sustainability framework. Insurance: Mathematics and Economics 69:117–126.

THE SURVIVOR DIVIDEND TO ENHANCE PENSION ADEQUACY INNOTIONAL DEFINED CONTRIBUTION SCHEMES
M. Carmen Boado-Penas1,∗ , Séverine Arnold (-Gaille)2
1 Department of Actuarial Mathematics and Statistics, Heriot-Watt University and and the Maxwell

Institute for Mathematical Sciences, Edinburgh (United Kingdom)
2 Faculty of Business and Economics, University of Lausanne (Switzerland)c.boado@hw.ac.uk (∗ corresponding author)
The mechanisms of non-financial defined contribution pension schemes (NDCs) are close to those of a fully
funded defined contribution plan but under a pay-as-you-go framework. Of particular interest is how theaccumulated capital of a deceased person is used, when the death occurs prior to retirement. At the moment,
Sweden is the only NDC country that distributes this capital, called survivor dividend (SD). Without a
distribution of the SD the scheme would accumulate a reserve with no clear purpose. This paper aims toanalyse to what extent the SD kept by most NDCs can be used to improve pension adequacy giving lowincome pensioners the financial support they need. We develop theoretical models to achieve the financial
equilibrium of the scheme depending on how the SD is distributed among all socio-economic groups andthe use of different mortality tables (unisex versus group-specific). Our results indicate that the survivor
dividend can be used to set up a minimum pension that benefit 66.54% of the pensioners increasing the
average annual pension by 8.68%.
Keywords: pension adequacy · notional defined contribution · pay-as-you-go · public pensions · socioeconomic groups

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Author index
Chen, Yunzhou, 66
Chuang, Shu-Yi, 85
Claramunt, Merce, 70
Clare, Andrew, 109
Colpo, Fabio, 67
Costabile, Massimo, 89
Craciunescu, Andrei, 47
Criens, David, 111

Abdelrahman, Hassan, 43
Aburto Barrera, Laura Iveth, 95
Aka, Samira, 107
Albrecher, Hansjoerg, 72, 92
Alcoforado, Hudo L.S.G., 97
Alcoforado, Renata G., 37, 97
Aragona, Maria, 84
Arandjelović, Aleksandar, 100
Arık, Ayşe, 57, 98
Arnold, Séverine, 17, 71, 120
Assa, Hirbod, 66
Ayuso, Mercedes, 79
Azcue, Pablo, 72

de Melo, Eduardo F.L., 82
De Mori, Luca, 42
Deelstra, Griselda, 78
Delong, Łukasz, 44, 62
Demartis, Stefano, 27
Denuit, Michel, 54
Devi Makam, Vaishno, 22
Devolder, Pierre, 65
Dhaene, Jan, 63
Dias, Alexandra, 88
Dimitrova, Dimitrina S., 94
Dodd, Erengul, 98
dos Reis, Alfredo D. Egı́dio, 37, 97
Doumen, Kristien, 49
Duncan, Ian, 99

Bacinello, A.R., 55
Badescu, Andrei, 43
Barbiero, Alessandro, 115
Barrieu, Pauline, 108
Baser, Furkan, 28
Bathke, Theis, 31
Belhouari, Oussama, 65
Bergel, Agnieszka I., 37
Bettels, Sören, 25
Bjørner Søe, Julie, 32
Bladt, Martin, 59, 69
Boado-Penas, M. Carmen, 19, 120
Boj, Eva, 34
Boutsikas, M.V., 78
Bozikas, Apostolos, 36, 58

Economides, D.-J., 78
Eisenberg, Julia, 67, 100, 101
El Meknouzi, Laila, 49
Empacher, Christina, 114
Escobar, Debora Daniela, 66

Cairns, Andrew, 57, 98
Carcache Flores, Roberto, 105
Cardoso, Rui M.R., 37
Cespedes, Luis, 79
Chang, Fang-Chi, 85
Chang, Yun-Tuan, 85
Chao, Chia-Chih, 85
Charpentier, Arthur, 30
Chaudhry, Atibhav, 63
Chen, Yining, 108

Fabrykowski, Lukas, 101
Fernandes Merchado, Agathe, 30
Fidelis, André P.F., 97
Fino, Elisabete, 67
Fonseca Diaz, Ivan, 17, 71
French, Declan, 81
Fung, Tsz Chai, 94
Furrer, Christian, 62
Gallic, Ewen, 30
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Garrido, José, 21, 43, 73
Gaspar, Raquel, 111
Gatti, Selim, 60
Goffard, Pierre-Olivier, 54
González-Vila, Laura, 34
Goudenege, Ludovic, 113
Gouthon, Jean-Luc, 43
Graziadei, Helton, 82
Grzelak, Lech A., 78
Günther, Sascha, 84, 117
Guerra, Manuel, 67, 101
Guillén, Montserrat, 23, 52
Guo, Betty, 75

Koch, Erwan, 92
Korn, Ralf, 48, 76, 102
Kouis, Panayiotis, 105
Kratz, Marie, 104, 107
Kukush, Alexander, 63Haberman, Steven, 42
Hainaut, Donatien, 64
Hannon, James, 81
Hatzopoulos, Peter, 58
Havrylenko, Yevhen, 51
Heras Martı́nez, Antonio J., 73
Hernández-Pacheco, Abraham, 105
Hieber, Peter, 84, 117
Hillairet, Caroline, 118
Hitaj, Asmerilda, 115
Hornung, Philipp C., 117
Huang, Chiao-Ching, 85
Huang, Yu-Kai, 85

Macdonald, Angus S., 98
Maggistro, R., 55
Makariou, Despoina, 108
Malavasi, Matteo, 29
Marino, M., 55
Marti, Joachim, 95
Melnikov, Alexander, 75
Milhaud, Xavier, 21, 43
Milidonis, Andreas, 105
Millossovich, Pietro, 22, 42
Molent, Andrea, 113
Moreno-Franco, Harold A., 39
Motte, Edouard, 64
Moura, Alexandra, 67, 86
Mouzourides, Petros, 105
Mrad, Mohamed, 118
Müller, Alaric J.A., 92
Müller, Alfred, 116
Muler, Nora, 72
Murat Mert, Ozenc, 102
Muromachi, Yukio, 24
Mwizere, Jean René, 109Mármol, Maite, 34Lai, Po-Hua, 85
Lee, Yu-Chen, 85
Lin, Sheldon, 43
Linders, Daniel, 63, 65
Loisel, Stéphane, 17Loke, Sooie-Hoe, 99
Londoño, Jaime A., 32

Iversen, Emma, 47
Jang, Jiwook, 29
Jeong, Himchan, 94
Jessop, Nick, 19
Kaakai, Sarah, 118
Kaishev, Vladimir K., 94
Kamps, Udo, 114
Kanellopoulos, Lazaros, 38
Karaman, Funda, 56
Kelbert, Mark, 39
Keller-Ressel, Martin, 110
Kim, Sojung, 25
Kleinow, Torstein, 87
Koc, Oguz, 28

Naveau, Philippe, 107
Neophytou, Marina, 105
Nguyen, Phuong, 101
Nicolet, Anna, 95
Nielsen, Jens Perch, 52122European Actuarial Journal Conference 2024
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Streftaris, George, 57, 98
Szatkowski, Marcin, 44

Nurkanović, Ajla, 48
O’Hagan, Adrian, 81Özalp, Mustafa Asım, 45
Özen, Selin, 40Øhlenschlæger, Christoffer, 59
Olivieri, Annamaria, 87
Olympio, Anani, 21
Owadally, Iqbal, 109

Targino, Rodrigo S., 82
Tenório, Pedro A., 97
Trück, Stefan, 29
Trufin, Julien, 54
Tsanakas, Andreas, 22
Tzougas, George, 19, 94
Ugarte Montero, Andrey, 87

Papachristos, Apostolos, 36, 39
Peleg, Nadav, 92
Peters, Gareth W., 29, 54, 99
Piette, Pierrick, 54
Pitselis, Georgios, 93
Pogorelov, Nikolai P., 39
Politis, Konstadinos, 39

van Berkum, Frank, 87
Van Liedekerke, Luc, 49
Van Lokeren, Mark, 91
Varea, Xavier, 34
Vellekoop, Michel, 87
Vergeynst, Jenna, 49
Vidal-Llana, Xenxo, 23
Vilar-Zanón, José L., 19, 73

Quinn, Barry, 81
Ramadani, Laurena, 76
Rodrigues, Diogo, 86
Rodriguez-Martinez, Eugenio V., 37
Rogo, Barbara, 27, 89
Russo, Emilio, 89

Wagner, Joël, 95
Wang, Chia-An, 85
Weber, Stefan, 25
Wei, Xiao, 113
Wolf, Felix L., 78
Wüthrich, Mario, 60, 62

Sachse, Felix, 110Şahin, Şule, 40, 45
Santolino, Miguel, 79
Scherer, Matthias, 47, 68
Schmeck, Maren, 101
Schmidt, Thorsten, 111
Schmiedt, Anja Bettina, 114
Selçuk-Kestel, A. Sevtap, 28, 102
Shao, Adam, 98
Shevchenko, Pavel V., 29
Siggelkow, Constantin, 68
Snels, Femke, 49
Sofronov, Georgy, 29
Solomou, Marina, 105
Spreeuw, Jaap, 94
Staino, Alessandro, 89
Stefanutto, Alessandro A., 97
Steffensen, Mogens, 117

Yánez, Juan Sebastián, 52
Yeh, Chin-Jung, 85
Yildirak, Kasirga, 45
Yslas, Jorge, 69
Zanette, Antonino, 113
Zhou, Nan, 19, 73
Zhu, Rui, 42

123

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024

Speaker index
Abdelrahman, Hassan, 43
Aburto Barrera, Laura Iveth, 95
Aka, Samira, 107
Alcoforado, Renata G., 37, 97
Arandjelović, Aleksandar, 100
Arık, Ayşe, 98
Arnold, Séverine, 17

Garrido, José, 21
Gatti, Selim, 60
Goffard, Pierre-Olivier, 54
González-Vila, Laura, 34
Graziadei, Helton, 82
Günther, Sascha, 117
Guo, Betty, 75

Barbiero, Alessandro, 115
Bathke, Theis, 31
Belhouari, Oussama, 65
Bjørner Søe, Julie, 32
Boado-Penas, M. Carmen, 120
Bozikas, Apostolos, 36

Hannon, James, 81
Hatzopoulos, Peter, 58
Havrylenko, Yevhen, 51
Hieber, Peter, 84
Hornung, Philipp C., 117
Jessop, Nick, 19

Carcache Flores, Roberto, 105
Cespedes, Luis, 79
Chao, Chia-Chih, 85
Charpentier, Arthur, 30
Chaudhry, Atibhav, 63
Claramunt, Merce, 70
Colpo, Fabio, 67
Costabile, Massimo, 89
Craciunescu, Andrei, 47

Kaakai, Sarah, 118
Kamps, Udo, 114
Kanellopoulos, Lazaros, 38
Karaman, Funda, 56
Koc, Oguz, 28Kratz, Marie, 104
Loisel, Stéphane, 17
Makariou, Despoina, 108
Malavasi, Matteo, 29
Marino, M., 55
Milhaud, Xavier, 43
Millossovich, Pietro, 22
Moreno-Franco, Harold A., 39
Motte, Edouard, 64
Müller, Alaric J.A., 92
Müller, Alfred, 116
Muler, Nora, 72
Murat Mert, Ozenc, 102
Muromachi, Yukio, 24
Mwizere, Jean René, 109

De Mori, Luca, 42
Deelstra, Griselda, 78
Delong, Łukasz, 62
Demartis, Stefano, 27
Dias, Alexandra, 88
Doumen, Kristien, 49
Duncan, Ian, 99
Economides, D.-J., 78
Eisenberg, Julia, 101
Escobar, Debora Daniela, 66
Fino, Elisabete, 67
Fonseca Diaz, Ivan, 71
Furrer, Christian, 62

Nguyen, Phuong, 101
Nurkanović, Ajla, 48
124

European Actuarial Journal Conference 2024
CEMAPRE/ISEG, Lisbon, September 9 – 11, 2024Özalp, Mustafa Asım, 45Øhlenschlæger, Christoffer, 59
Olivieri, Annamaria, 87
Pitselis, Georgios, 93
Politis, Konstadinos, 39
Ramadani, Laurena, 76
Rodrigues, Diogo, 86
Rogo, Barbara, 89
Sachse, Felix, 110Şahin, Şule, 40
Schmidt, Thorsten, 111
Siggelkow, Constantin, 68
Solomou, Marina, 105
Spreeuw, Jaap, 94
Streftaris, George, 57
Szatkowski, Marcin, 44
Trufin, Julien, 54
Tzougas, George, 94
Ugarte Montero, Andrey, 87
Van Lokeren, Mark, 91
Vidal-Llana, Xenxo, 23
Weber, Stefan, 25
Yánez, Juan Sebastián, 52
Yslas, Jorge, 69
Zanette, Antonino, 113
Zhou, Nan, 19, 73

125