bluuebunny/crossref_metadata_2025 huggingface dataset:
Indirect forcing of black carbon on clouds over northeast India
Authors: Panicker A. S. , Pandithurai G. , Safai P. D. , Prabha T. V.
Published: July 2016

Black carbon (BC) induced indirect radiative forcing and cloud albedo effect has been studied for the first time over northeast India. Measurements of BC and cloud microphysical parameters were carried out during Phase‐I of the Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) over northeast India (Guwahati) in 2009. Liquid water path (LWP) in the cloud layers coherent with BC on different experimental days was found to be 206–327 g m−2 over the region. Black carbon aerosol indirect effect (BCIE) for fixed LWP is found to be 0.32–0.48 on different days of observations. The indirect forcing corresponding to this BCIE has been estimated using a radiative transfer model for fixed LWP by altering the derived BC‐AOD (aerosol optical depth from measured BC profiles) and cloud effective radius (Re) combinations. The estimated average BC‐induced indirect forcing (BCIF) was −24 to −37.1 W m−2 at the surface and +2.5 to +14.8 W m−2 at the top of the atmosphere (TOA). The average albedo due to BCIF at TOA was 0.49–0.61. BCIF is found to reduce the cloud reflection by 1.5–2% over the region. The sensitivities of cloud parameters to BCIF and the albedo effect are illustrated.
Assessment and tuning of data assimilation systems using passive observations
Authors: Marseille Gert‐Jan , Barkmeijer Jan , de Haan Siebren , Verkley Wim
Published: July 2016

Independent observations can be used to diagnose and tune a data assimilation (DA) system. Analysis increments generally improve the model state near assimilated observations but degrade it further away. High‐resolution aircraft observations from Mode‐S Enhanced Surveillance (Mode‐S EHS) are used as an independent data source to verify increment degradation as a function of distance from assimilated observations. An adaptation of the inherently imperfect gain matrix in DA is proposed such that resulting analyses better fit the independent data source and as such draw model simulations closer to the true atmospheric state. It is found that the structure functions of the background‐error covariance matrix of the experimental mesoscale HARMONIE model are appropriate but too much weight is given to observations relative to the model background. The ECMWF model is well tuned with a slight overestimation of temperature information in the upper troposphere.

Finally, a caveat is highlighted when comparing model forecasts from different experiments against observations. It is common practice to use the same observing system both in the analysis and for forecast verification. However, forecast verification is prone to sampling errors, yielding less favourable scores when using an independent data source. Avoidance of biased conclusions on the impact of observing systems, e.g. in observing system experiments (OSE), requires an independent data source (best practice) or a data source used in all experiments (best pragmatic practice) for verification of forecasts from different experiments.
Simulation of incompressible multiphase flows with complex geometry using etching multiblock method
Authors: Liu Haoran , Mu Kai , Ding Hang
Published: July 2016

The incompressible two-phase flows are simulated using combination of an etching multiblock method and a diffuse interface (DI) model, particularly in the complex domain that can be decomposed into multiple rectangular subdomains. The etching multiblock method allows natural communications between the connected subdomains and the efficient parallel computation. The DI model can consider two-phase flows with a large density ratio, and simulate the flows with the moving contact line (MCL) when a geometric formulation of the MCL model is included. Therefore, combination of the etching method and the DI model has potential to deal with a variety of two-phase flows in industrial applications. The performance is examined through a series of numerical experiments. The convergence of the etching method is firstly tested by simulating single-phase flows past a square cylinder, and the method for the multiphase flow simulation is validated by investing drops dripping from a pore. The numerical results are compared with either those from other researchers or experimental data. Good agreement is achieved. The method is also used to investigate the impact of a droplet on a grooved substrate and droplet generation in flow focusing devices.
A CORRELATION SENSITIVITY ANALYSIS OF NON-LIFE UNDERWRITING RISK IN SOLVENCY CAPITAL REQUIREMENT ESTIMATION
Authors: Bermúdez Lluís , Ferri Antoni , Guillén Montserrat
Published: July 2016

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the solvency capital requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the standard model approach. Alternatively, the requirement is then calculated using an internal model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR, we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.
The Stress Field Due to an Edge Dislocation Interacting With Two Circular Inclusions
Authors: Chao C.-K. , Chen F.-M. , Lin T.-H.
Published: July 2016

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.
Radiocarbon Variation in Charcoal/Wood and Soil Fractions from a Loessic Setting in Central Alaska
Authors: Reuther Joshua D , Cherkinsky Alexander , Coffman Sam
Published: July 2016

The Healy’s Lucky Strike site in central Alaska has an exceptional Holocene loess-paleosol sequence that has afforded us the ability to look at variation in14C dating of soil organic matter (SOM) fractions in a high-latitude loess setting. Our work has focused on comparing the radiocarbon ages of charcoal and wood to base-soluble humic acids (HA) and base-insoluble soil residue (SR) fractions from bulk soil samples. Charcoal/wood ages were younger than HA ages reflecting the later stages of vegetation development at the surface of the soils prior to being covered by loess accumulation; the HA ages generally reflect the overall timing of soil formation and mean residence time of SOM. Soil residue ages are older than charcoal/wood and HA ages. SOM ages at this location become increasingly older than charcoal/wood ages with depth, reaching 750 to 8070 yr in difference and associated with weakly developed soils at the lowest depths. We suggest the drastic SOM age differences at this site result from the differential incorporation of small particles of coal throughout the sedimentary matrices introduced older contaminants to SR fractions.
Genetic differences amongHaplorchis taichuipopulations in Indochina revealed by mitochondrialCOX1sequences
Authors: Thaenkham U. , Phuphisut O. , Nuamtanong S. , Yoonuan T. , Sa-nguankiat S. , Vonghachack Y. , Belizario V.Y. , Dung D.T. , Dekumyoy P. , Waikagul J.
Published: July 2016

Haplorchis taichuiis an intestinal heterophyid fluke that is pathogenic to humans. It is widely distributed in Asia, with a particularly high prevalence in Indochina. Previous work revealed that the lack of gene flow between three distinct populations of VietnameseH. taichuican be attributed to their geographic isolation with no interconnected river basins. To test the hypothesis that interconnected river basins allow gene flow between otherwise isolated populations ofH. taichui, as previously demonstrated for another trematode,Opisthorchis viverrini, we compared the genetic structures of seven populations ofH. taichuifrom various localities in the lower Mekong Basin, in Thailand and Laos, with those in Vietnam, using the mitochondrial cytochromecoxidase subunit 1 (COX1) gene. To determine the gene flow between theseH. taichuipopulations, we calculated their phylogenetic relationships, genetic distances and haplotype diversity. Each population showed very low nucleotide diversity at this locus. However, high levels of genetic differentiation between the populations indicated very little gene flow. A phylogenetic analysis divided the populations into four clusters that correlated with the country of origin. The negligible gene flow between the Thai and Laos populations, despite sharing the Mekong Basin, caused us to reject our hypothesis. Our data suggest that the distribution ofH. taichuipopulations was incidentally associated with national borders.
UNIFORM CONVERGENCE RATES OF KERNEL-BASED NONPARAMETRIC ESTIMATORS FOR CONTINUOUS TIME DIFFUSION PROCESSES: A DAMPING FUNCTION APPROACH
Authors: Kanaya Shin
Published: July 2016

In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya–Watson type, introducing a new technical device called adamping function. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support, and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also be of some independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non/semiparametric estimation and testing problems of diffusion processes.
Natural disturbance, vegetation patterns and ecological dynamics in tropical montane forests
Authors: Crausbay Shelley D. , Martin Patrick H.
Published: July 2016

Disturbance is a central process in forest dynamics, yet the role of natural disturbance in tropical montane forests (TMFs) has not been systematically addressed. We posit that disturbance in TMFs has a wider role than commonly acknowledged and its effects are distinctive because: (1) TMFs often have very low rates of productivity due to low resources, and so recovery from disturbance may be slow, (2) montane forests have marked environmental heterogeneity which interacts with disturbance, (3) a large percentage of TMFs are regularly exposed to high energy windstorms and landslides, and (4) TMFs contain a biogeographically rich mixture of tree species with divergent evolutionary histories that interact differently with different disturbance types. We reviewed the literature on natural disturbance in TMFs and found 119 peer-reviewed papers which met our search criteria. Our review shows that disturbance is widespread in TMFs with pronounced effects on structure, function, composition and dynamics. Disturbance is also evident in the ecology of TMF biota with clear examples of plant life-history traits adapted to disturbance, including disturbance-triggered germination, treefall gap strategies and resprouting ability. Important aspects of TMF disturbances are stochastic and site-specific, but there are broad patterns in disturbance type, frequency and severity along latitudinal, altitudinal and environmental gradients. Compared with the lowland tropics, TMF disturbances are more spatially structured, TMFs experience more disturbance types in a given area due to environmental complexity, and TMFs are much more prone to small-scale yet severe landslides as well the large and potentially catastrophic disturbances of cyclones, forest die-back and fire. On the whole, natural disturbance should assume a larger role in models of ecosystem processes and vegetation patterns in TMFs. An improved understanding of what creates variation in disturbance severity and post-disturbance recovery rates, how composition and diversity feedback on disturbance type and likelihood, and how global change will alter these dynamics are important priorities in future TMF ecology research.
L1 EXPLICIT INSTRUCTION CAN IMPROVE L2 ONLINE AND OFFLINE PERFORMANCE
Authors: McManus Kevin , Marsden Emma
Published: July 2016

This study investigated the effectiveness of providing L1 explicit information (EI) with practice for making more accurate and faster interpretations of L2 FrenchImparfait(IMP). Two treatments were investigated: (a) “L2-only,” providing EI about the L2 with L2 interpretation practice, and (b) “L2+L1,” providing the exact same L2-only treatment and including EI about the L1 (English) with practice interpreting L1 features that are equivalent to the IMP. Fifty L2 French learners were randomly assigned to either L2-only, L2+L1, or a control group. Online (self-paced reading) and offline (context-sentence matching) measures from pretest, posttest, and delayed posttests showed that providing additional L1 EI and practice improved not only offline L2 accuracy, but also the speed of online L2 processing. To our knowledge, this makes original and significant contributions about the nature of EI with practice and the role of the L1 (Tolentino & Tokowicz, 2014), and it extends a recent line of research examining EI effects in online sentence processing (Andringa & Curcic, 2015).
A Note on the Most “Dangerous” and Skewest Class of Distributions
Authors: Benktander Gunnar
Published: July 2016

In the classical definition skewness is departure from symmetry. It was therefore natural to measure skewness by using a normalized third moment μ3/σ3. This condensed measure, however, is not refined enough to be used as an operational instrument for studying various functions which might be used to describe actual claim distributions. This is true especially when the interest is concentrated towards the higher values of the variate.

In their paper (1) Benktander-Segerdahl have suggested that the average excess claim m(x) as a function of the priority x should be used to reveal the characteristics of the tail of the distribution

where P(x) = 1 — H(x) denotes the distribution function.

This statistic is very apt when comparing actual claim distributions with possible theoretical models. It is also useful when classifying these models.

If, however, emphasis mainly is laid on classifying distributions according to their skewness, another statistic might be preferable. Let μ(x)dx denote the probability that a stochastic variable which is known to be at least equal to x, does not exceed x+dx. In other words, μ(x)dx represents the probability that a claim or the corresponding stochastic variable, which, when observed from the bottom, is “alive” at x, “dies” in the interval (x, x + dx). The lower this claims rate of mortality, the skewer and more dangerous is the claim distribution.
On the Difference between the Concepts “Compound” and “Composed” Poisson Processes
Authors: Philipson Carl
Published: July 2016

In the discussion in the ASTIN Colloquium 1962, which followed my lecture on the numerical evaluation of the distribution functions defining some compound Poisson processes, a remark was made, which drew my attention to the paper quoted here below under reference number (1), On composed Poisson distributions I.

As I have the impression that this remark may induce some confusion of the terms “compound” and “composed”, the more as the same French word (composé) is used for the two terms, a comparison between the two kinds of processes shall be made.

1. The most general propositions of (1) are a theorem which concerns a general homogeneous Markoff process (1.c. § 2) and a theorem for the family {P(k,p)} of distribution functions of positive integervalued variables with mean p, where p runs over all non-negative numbers, and where the convolution of P(k,p1) and P(k,p2) is equal to P(k,p1 + p2) (l.c. § 3). By these propositions the characteristic functions corresponding in the 1st case to the distribution functions defining the homogeneous Markoff process, and in the 2nd case to the distribution functions belonging to the family {P(k,p)} can all be written in the same form, namely

where u is an entirely imaginary variable, p is the parameter of the process, respectively of P(k,p) and c1, c2 … non-negative constants such that converges. If, in the 1st case, converges, and as, in the 2nd case, this series converges, the distributions defined by these characteristic functions are called composed Poisson distributions, which define homogeneous composed Poisson processes.
The unearned no claim bonus
Authors: Welten C. P.
Published: July 2016

1. The claims experience of a motorcar insurance is assumed to give some indication about the risk (basic claim frequency) of that insurance. The experience rating systems in motor insurance are based on this supposition. In these systems the premium to be paid in some year is a function of the individual claims experience of preceding years. That premium can be considered as the difference between:

— a basic premium, being the expected value of the premium to be paid for insurances with a basic claim frequency equal to the mean value of the basic claim frequency of the portfolio or the tariff class.

— a positive or negative bonus; although in the negative case the word bonus is misleading this word will nevertheless be used for both cases in this paper.

The bonus usually consists of at least the following components:

a. a component concerning the individual claim frequency.

b. an individual random factor.

c. a collective random factor.

Other factors, like the effect of the trend in the claim frequencies and the effect of the dependence of the claim frequency of age and experience of the driver are not taken into account in this paper.

2. The meaning of the three components mentioned in section I can be demonstrated by the following example.

The structure function U(χ) of the portfolio, being the distribution function of the individual basic claim frequencies χ is assumed to be defined by

representing a gamma distribution with expected value q and variance qb. The probability Pi for an insurance to have i claims in a certain year is supposed to be

In this formula the factor y has the same value for all insurances in the portfolio in a certain year but varies from year to year according to the distribution function G(y) with expected value 1 and variance .
Driving with markov-programming
Authors: de Leve G. , Weeda P. J.
Published: July 2016

Let us consider the following problem.

A motorist has decided to effect an accident insurance under the following conditions. The insurance runs for one year. The premium for the first year amounts E0. If no damages have been claimed during i successive years, i = 1, 2 or 3 the premium is reduced to Ei. After four years of damagefree driving no further premium reduction is granted, so the premium remains E3. The premium is due on the first day of the year. The own risk amounts a0.

The number of accidents of our motorist during a time period T is assumed to be Poisson distributed with parameter λT. The extent of the damage has distribution function F(s) with finite mean and variance.

The problem of our motorist will be to decide whether to claim a damage or not. He will have to develop a strategy that specifies his decisions in every possible situation. His strategy will be called optimal if it minimizes the expected costs in the long run.

We may expect that in view of the premium reduction, it will be unprofitable to claim damages which are not much larger than a0. Once a damage is claimed it will be profitable to claim all following damages that exceed a0 during the remaining part of the year.

Hence his decisions will also depend on the time of the year and the premium paid at the beginning of that year. So we distinguish between four types of years, for each premium one.
Large Claims in Insurance Mathematics
Authors: Teugels Jef L.
Published: July 2016

I take great pleasure in addressing this audience. As you might know I'm a mathematician with a deep interest in insurance mathematics. As such, it is my sincere opinion that the gap between practising actuaries and theoretical researchers can be made substantially smaller. If my contribution can help in bridging the gap, I will feel fully compensated for the effort it took to prepare this lecture and the results contained therein.

The simple fact that we meet on the occasion of the sixteenth ASTIN Colloquium gives me a challenging opportunity to help in creating a platform on which both theoreticians and practitioners can meet.

The subject of my lecture stems from a long interest in large claims: What are they? Are they really dangerous? Is there a way to get them under control? Can one recognize them in practical situations?

I like to express in simple mathematical terms some results that might help in acquiring better insight on the impact of large claims in insurance mathematics. Perhaps, no result will be of immediate applicability as reality is too complicated to be described by the simplicity of the results to follow. Nevertheless the latter can be considered as building blocks of a real world in which one has to tackle large claims in theory as well as in practice.
A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities
Authors: Goovaerts Marc , de Vylder Florian
Published: July 2016

Probabilities of ruin are solutions of differential or integrodifferential equations. Solving such equations numerically can be performed by means of approximate quadrature formulae for the convolution part of the equation. In this contribution it is shown how applicable recursion formulae, giving results within a prescribed tolerance level, can be obtained. Some numerical results are displayed.
Homogeneous Premium Calculation Principles
Authors: Reich Axel
Published: July 2016

A premium calculation principle π is called positively homogeneous if π(cX) = cπ(X) for all c > 0 and all random variables X. For all known principles it is shown that this condition is fulfilled if it is satisfied for two specific values of c only, say c = 2 and c = 3, and for only all two point random variables X. In the case of the Esscher principle one value of c suffices. In short this means that local homogeneity implies global homogeneity. From this it follows that in the case of the zero utility principle or Swiss premium calculation principle, the underlying utility function is of a very specific type.

A very general theorem on premium calculation principles which satisfy a weak continuity condition, is added. Among others the proof uses Kroneckers Theorem on Diophantine Approximations.
Rate Making and Society's Sense of Fairness
Authors: de Wit G. W. , van Eeghen J.
Published: July 2016

Actuaries have always been in search of ways to determine premiums which match the risks insured as closely as possible. They do this by differentiating between them on the basis of observable risk factors. In practice, many examples of such risk factors are being used: age and sex for life insurance; location, type of building etc. for fire insurance. Motor insurance is perhaps the most characteristic branch with respect to this phenomenon: in tariffs we find factors like weight, price or cylinder capacity of the car, age of the driver, area of residence, past claims experience (Bonus/Malus), annual mileage etc.

Outsiders may not always be very positive about such a refined premium differentiation. The basis of insurance, they say, should be solidarity among insureds; premium differentiation is basically opposed to this. Another statement heard in the field is: “Premium differentiation ultimately results in letting every individual pay his own claims, it is the end of insurance”.

Much confusion arises during discussions about this subject, especially between actuaries and non-actuaries. We will therefore first give a mathematical definition of solidarity, (Section 2), followed by a brief description of certain trends in society which might bring insurers to deliberately drop certain risk factors from their tariffs in order to increase solidarity (Section 3). The consequences of doing so are examined and it is shown that increased solvency requirements will in the end prove to be ineffective. A possible solution is a voluntary transfer of premium between companies (Section 4). The situation is illustrated by an example of health insurance in the Netherlands, where proposals to arrive at such transfeis are presently being discussed.
Optimal Risk Exchanges
Authors: Bühlmann Hans , Jewell William S.
Published: July 2016

The determination of optimal rules for sharing risks and constructing reinsurance treaties has important practical and theoretical interest. Medolaghi, de Finetti, and Ottaviani developed the first linear reciprocal reinsurance treaties based upon minimizing individual and aggregate variance of risk. Borch then used the economic concept of utility to justify choosing Pareto-optimal forms of risk exchange; in many cases, this leads to familiar linear quota-sharing of total pooled losses, or to stop-loss arrangements. However, this approach does not give a unique, risk-sharing agreement, and may lead to substantial fixed side payments. Gerber showed how to constrain a Pareto-optimal risk exchange to avoid invasion of reserves.

To these ideas, the authors have added the actuarial concept of long-run fairness to each participant in the risk exchange; the result is a unique, Pareto-optimal risk pool, with “quota-sharing-by-layers” of the total losses. There are many interesting special cases, especially when all individual utility functions are of exponential form, giving linear quota-sharing-by-layers. Algorithms and numerical examples are given.
The Credible Distribution
Authors: Jewell William S.
Published: July 2016

Credibility theory is concerned with the problem of forecasting the mean performance (claim frequency, total losses, etc.) of an individual risk, selected from a collective of heterogeneous risks, based upon the statistics of the collective, and upon the individual's experience data. The classic results, derived by American actuaries in the 1920's, were further strengthened by Bailey and Mayerson in 1950 and 1965, who showed that these results were exact Bayesian for certain risk distributions. Bühlmann, in 1967, then showed that the credibility formulae were the best least-squares linearized approximation to the exact Bayesian forecast, for general risk distributions.

This paper extends credibility theory to the problem of forecasting thedistributionof individual risk, based upon collective statistics and individual experience data. Although the problem is, in principle, solved by finding a Bayesian conditional distribution, this approach requires a detailed knowledge of collective structure. Thecredible distribution, on the other hand, requires fewer prior statistics, and is also a best least-squares linearized approximation to the exact Bayesian distribution.

Following the theoretical development, detailed computational results are given.
Extreme Value Theory and Large Fire Losses
Authors: Ramachandran G.
Published: July 2016

The statistical theory of extreme values well described by Gumbel [1] has been fruitfully applied in many fields, but only in recent times has it been suggested in connection with fire insurance problems. The idea originally stemmed from a consideration of the ECOMOR reinsurance treaty proposed by Thepaut [2]. Thereafter, a few papers appeared investigating the usefulness of the theory in the calculation of an excess of loss premium. Among these, Beard [3, 4], d'Hooge [5] and Jung [6] have made contributions which are worth studying. They have considered, however, only the largest claims during a succession of periods. In this paper, generalized techniques are presented which enable use to be made of all large losses that are available for analysis and not merely the largest. These methods would be particularly useful in situations where data are available only for large losses.
Experience Rating with Credibility Adjustment of the Manual Premium
Authors: Taylor G. C.
Published: July 2016

A common procedure for experience rating is to use Whitney's credibility formula with the manual premium per risk unit estimated by the observed average claim amount per risk unit. As pointed out by Whitney himself, this observed average also needs to be subjected to credibility adjustment. This suggestion is pursued in the paper and an experience rating procedure developed in which there are two stages:

(i) revision of the prior expected manual premium in accordance with the observed average claim amount per risk unit;

(ii) experience rating of the individual risk classes by the usual methods but using the manual premium obtained in stage (i).

Both stages of this procedure involve credibility indices, for which formulae are developed.

Conditions under which the “common procedure” referred to above is fairly reliable are found and it is seen, somewhat surprisingly, that the procedure is often more valid than one expects on intuitive grounds. Care is necessary, however, when there are wide differences in size between different risk classes.
Economic Factors in Liability and Property Insurance Claims Costs
Authors: Masterson Norton E.
Published: July 2016

The original paper with this title was published in 1968, following presentation at a Casualty Actuarial Society meeting. This is another up-date of indexes in the economic model—first report of 1976 and a forecast for 1977. These LPI indexes measure economic factors affecting loss and loss adjustment settlement costs which are incurred after claims have been reported. The indexes measure direct claims costs and not the reinsured excess losses which would be more adversely affected by inflation.

This is a Claims Market Place concept of the loss settlement function of the insurance company. Claims Costs (our economic cost of production) result from purchasing of services under unusual circumstances in controversial, severe, hasty and often emergency situations. Claims settlements can take place in court rooms, lawyers' offices, repair garages and hospitals. The legalistic atmosphere is often one of friction and excessive demand rather than of a normal commercial esprit de corps. The procurement of these claims services requires dealing with high cost furnishers of services: doctors, clinics, hospitals, lawyers, repair garages or body shops, building trades, house furnishings.
Earthquake Insurance in Japan
Authors: Wakuri Masao , Yasuhara Yasuyuki
Published: July 2016

Japan is one of the most earthquake-prone countries in the world and a considerable volume of earthquake insurance is written by private insurers. Therefore, a report on earthquake insurance in Japan has been prepared for the 13th ASTIN Colloquium.

We will first summarise, from recent results of seismological studies, the matters which would form the basis for a study of earthquake insurance, and then explain how this insurance actually works in Japan.
Survival Probabilities Based on Pareto Claim Distributions
Authors: Seal Hilary L.
Published: July 2016

It is commonly thought that the characteristic function (Fourier transform) of the Pareto distribution has no known functional form (e.g. Seal, 1978, pp. 14, 40, 57). This is quite untrue. Nevertheless the characteristic function of the Pareto density is conspicuously absent from standard reference works even when the Pareto distribution itself receives substantial comment (e.g. Haight, 1961; Johnson and Kotz, 1970, Ch. 19; Patel, Kapadia and Owen, 1976, § 1. 5).

The Pareto density may be written

with distribution function

mean = p/(v − 1) and variance = b2v(v − 1)2(v−2). These are infinite when v≤1 and v≤2, respectively. Its Laplace transform (s= c + iu)

where E is the generalized exponential integral (Pagurova, 1961) and can be written in terms of incomplete gamma or confluent hypergeometric functions (Slater, 1960, Sec. 5.6). When s = − it β(s) becomes the characteristic function (see Appendix I).

As Benktander (1970) tells us, the Pareto distribution has been particularly successful at representing the distribution of the larger claim amounts. In earlier years it was employed to represent the distribution of life insurance sums assured but more recently it has been used for the claim distributions of fire and automobile insurance. Table 1 provides the v-values we have been able to locate. Note that the variance of the distribution is infinite when v≤2 and if it were not for the anomalous v-values of Andersson (1971) we would have ventured the opinion that modern claim data encourage the assumption that v>2. In our numerical work we have used v = 2.7 and smaller values might change some of the computer rules we have proposed in Appendix II.
Evaluation of the Capacity of Risk Carriers by Means of Stochastic-Dynamic Programming
Authors: Pentikäinen T. , Rantala J.
Published: July 2016

The Ministry of Social Affairs and Health, being the Supervising Office of Insurance in Finland, has established a special working group to investigate the problems involved with the solvency of insurers. A report will be compiled in a near future. The capacity of risk carriers is one of the problems dealt with, and it will be preliminarily reviewed in this paper.

The problem was treated by the working group parallelly by means of

1. an empirical approach observing actual fluctuations in underwriting gains of insurers, and

2. a theoretical approach, constructing a stochastic-dynamic model and studying its behaviour, especially its sensitivity to numerous background factors.

First the methods of investigation are described and their application is then demonstrated using some numerical data. Because a comprehensive report will be published by the working group separately, only the main schedule is given. For the same reason the consideration is limited here to stochastic risks, omitting the fact that the solvency of an insurer is also jeopardized by numerous “non-stochastic” risks such as failure in investments, political interference of the authorities, mismanagement of the company, or misappropriation of its property.
The Bargaining Set of a Reinsurance Market
Authors: Baton Bernard , Lemaire Jean
Published: July 2016

This paper uses the same notations and some of the results of Baton and Lemaire (1981). The reader is referred to that work for more details about the classical risk exchange model, which will not be recalled here. The main result of that former paper was to characterize the core of the market in the case of exponential utilities, and to show that it is never empty. Since the core always exists, and since it is such an intuitive notion, one might wonder why we introduce here a much more complicated concept. The reason is that the core is presently subject to a heavy fire of criticisms–both experimental and theoretical–from leading researchers in game theory; they claim that the core is much too static, that it does not take into account the real dynamics of the bargaining process, that it does not introduce the full spectrum of negotiation threats of the traders. Indeed, experimental data consistently produce final payoffs that lie outside the core, but within the bargaining set (abbreviated: b.s.). We shall attempt to illustrate those criticisms in 4. We shall define the b.s. in a general non transferable game in 2, and characterize it in the special case of a 3-company reinsurance market in 3, but first of all we would like to explain intuitively the basic mechanisms of the b.s. by means of a simple example (with transferable utilities).

The basic difficulty in modelling a negotiation process is to express what is the purpose of the game. Certainly, the objective is not just to get the maximal amount of profits, because if everyone demands the highest payoff he can obtain in a coalition, no agreement will be reached; the goal of the process is to attain some state of stability, to which the bargainers should agree if they want any agreement to be enforced. This stability should reflect in some way the power of each player, which results from the rules of the game, his initial situation, his attitude towards risk, …

A bargaining process is a multi-criteria situation, in which the players certainly attempt to maximize their payoffs, but also try to enter into a “safe” or “stable” coalition.
Novelties in Swedish Automobile Insurance Rating
Authors: Lanteli Gunnar
Published: July 2016

On March 10th, 1961, the majority of the Swedish Automobile Insurance Companies introduced a remarkable novelty in automobile insurance rating, a rating plan for private passenger cars partly based on a recent statistical investigation of the variation of risk with some characteristics of the driver and the vehicle. These characteristics had not until then been used for classification purposes, nor had they been studied in our current experience.

For a long time the Swedish rating plan has classified private passenger cars by geographical district (3), merit class or „bonus class” (7) and (for Auto Physical Damage only) horsepowers (8). Teetotallers enjoy a special discount of 20%.

In spite of this rather far-going subdivision, founded on an elaborate statistical experience it was quite obvious that some important element was missing, as different companies operating in the same market showed significantly deviating underwriting experience. The tariff association „Svenska Bilförsäkringsföreningen” (SBF) and some other independent companies agreed to make a special investigation to find the cause of this adversity. A small committee was appointed to handle the question. From the start it was clear that some kind of inquiry had to be made among the policy holders of the participating companies. The information we needed was if and how different attributes such as sex, age, marital status, occupation, use of the car, annual mileage etc. influenced the risk. To inquire all of our private passenger carowners would have been too costly so we had to choose between a random sample and some other kind of limitation.
Quelques réflexions sur la réforme du tarif français d'assurance automobile
Authors: Thepaut Andre
Published: July 2016

Très nombreux sont les assureurs français qui paraissent admettre aujourd'hui la nécessité de réformer les méthodes actuelles de tarification de l'assurance automobile. De nos jours en effet la possession d'un véhicule automobile n'est plus le privilége de la classe bourgeoise aisée; de très nombreux petits fonctionnaires, employés, artisans et ouvriers tant à la ville qu'à la campagne considèrent un tel véhicule comme absolument indispensable à la vie moderne. Cet état d'esprit est particulièrement vrai chez les jeunes ménages pour lesquels le véhicule automobile se situe tout à fait au sommet de la hiérarchie des besoins, immédiatement après la chambre à coucher et bien souvent avant la salle de bains ou le frigidaire.

Pour mesurer l'ampleur du problème ainsi posé aux assureurs, il est utile d'examiner le tableau de l'annexe n° 1 extrait d'une étude récente faite par l'I.N.S.E.E. à la demande du centre de recherches et de documentation sur la consommation (C.R.E.D.O.C.) et publiée en Décembre 1960.

On constate notamment que:

1°/ sur 4.539.000 véhicules à 4 roues, 1.053.000 appartiennent à des ouvriers ou à du personnel de Service et 657.000 à des agriculteurs;

2°/ ces véhicules sont achetés d'occasion pour la plupart;

3°/ leur kilométrage annuel est très inférieur au kilométrage moyen général; autrement dit la dispersion des kilométrages autrefois relativement faible parait s'être accrue très considérablement ces dernières années.

Ces constatations expérimentales s'expliquent d'ailleurs aisément si l'on songe aux ressources limitées dont disposent ces “marginaux” de l'automile qui, d'ailleurs, ont bien souvent acheté leur vehicule à crédit.
Problems in Motor Insurance — Claim Reserves
Authors: Masterson Norton E.
Published: July 2016

In his comprehensive paper entitled “A General Survey of Problems Involved in Motor Insurance”, Dr. Carl Philipson includes remarks with respect to mathematical reserves. The purpose of this paper is to discuss a method of statistical estimation of Third Party Motor Insurance claim reserves. These methods can also be used for Car Damage Insurance, since reserve determination for these rapid settlement property coverages is simpler than for Third Party lines.

Dr. Philipson mentions the two main purposes of claim reservesbalance sheet loss reserves which shall be estimated on the safe side for financial reasons, and those reserves needed for risk statistics. In this paper I shall confine my subject to aggregate loss reserves for financial statements and internal management operating reports.

In this paper, it will be convenient to refer to both European and U.S. terminology for Motor Car and Automobile Insurance.

The comparable terms are:

The accident year is the important fiscal period underlying not only the statistical estimation methods discussed in this paper but it is also the basic grouping of accidents in the official reserve tests required in the Annual Statements of U.S. companies for casualty and property lines. An accident year embraces the entire population of claims incurred with accident dates in a particular calendar year, whether reported to the company in that year or subsequently (i.e., incurred /not reported).
Sur la détermination de la réserve pour sinistres en suspens dans l'assurance automobile
Authors: Molinaro Luigi
Published: July 2016

I) Parmi les différentes questions qui se posent dans l'étude de l'assurance automobile, celle de l'évaluation des réserves techniques est sans doute une des plus importantes. Dès que l'augmentation progressive du parc des véhicules a entraîné une hausse sensible de la chiffre des affaires et que le besoin de sauvegarder l'indemnisation des sinistres de circulation a transformé la base même du rapport contractuel, le problème des garanties, indissociable de celui de la solvabilité de l'entreprise, s'est imposé à l'attention générale.

En raison de cette évolution et de la nécessité d'un contrôle sur les engagements des compagnies, la fixation du montant exact de la réserve sinistres est fondamentale soit par rapport à la validité du tarif adopté (congruité des primes), soit à la possibilité de faire face aux engagements techniques moyennant des activités correspondantes. Deux aspects done d'un même problème, dont l'importance est augmentée dès que les risques se sont alourdis, les résultats de la branche défavorables, la situation économique et monétaire de plusieurs pays est devenue instable.

2) Le problème du calcul de la réserve pour sinistres en cours avait été posé, il y a plus que trente ans, par M. d'Addario: dans ses études il avait mis en relief l'existence d'une relation dans l'échelonnement des paiements valable pour une période de stabilité monétaire et d'une loi de distribution par rapport à l'âge du portefeuille sinistres (génération sinistres)). A cette oeuvre, disons prioritaire, ont suivi les remarquables travaux de M. M. Thépaut, Burlot, Henry, Pellegrin, Depoid: à la lumière des données expérimentales du marché français ils ont eu le grand mérite de pousser les études sur le coût moyen des sinistres et sur la cadence des règlements.
Random processes and their application to demography and insurance
Authors: Gnedenko B. W.
Published: July 2016

Mr. Chairman, Honourable Colleagues!

Let me thank the organisers of this symposium for the honour they have done me by inviting me to present my report before this eminent audience. I would also like to express my thanks to all who are present here for the confidence shown to me as rapporteur.

The genesis and development of the theory of random processes is closely related to the problems of demography and insurance. Numerous problems stimulating the development of the theory of probability and the theory of random processes—the latter constituting one of the essential parts of the modern theory of probability—are connected with these two fields of research and activity.

The theory of random processes, being stimulated—similarly to other fields of mathematics—by concrete practical tasks, has created the general ideas and methods of research, achieving many valuable results. With the passage of time, it appeared that the theory of random processes can be usefully applied, by its conceptions, results and methods, to a number of scientific fields and practical activity. Its conceptions have found wide and important application to the earlier crystallized fields of human knowledge, as well as to the newly appearing ones.

These new fields of mathematics serve us as an example which once more corroborate the thesis, well known to us, according to which the course of the development of human knowledge starts from empirical observations, then passes up to abstract thinking and finally to practice.
The ruin probability in a special case
Authors: Bohman H.
Published: July 2016

It is fantastic how the computer has changed our attitude to numerical problems. In the old days when our numerical tools were paper, pencil, desk calculator and logarithm tables we had to stay away from formulas and methods which led to too lengthy calculations. A consequence is that we have a tendency to think of numerical analysis in terms of the classical tools. If we go back to the results of earlier writers it seems, however, very likely that many results and formulas developed by them which had earlier a theoretical interest only could nowadays be applied successfully in numerical analysis.

As an example I take the ruin probability ψ(x). The Laplace transform of ψ(x) is given by the following expression

where c > 1. In fact (c — 1) is equal to the “security loading”. The function p(y) is equal to the Laplace transform of the claim distribution. We assume that the mean claim amount is equal to one, i.e. p′(0) = — 1.

In his book from 1955 [1] Cramer points out that this formula will be more easy to handle if the claim distribution is an exponential polynomial. In this case we have

where

Cramér's results are given on pages 81-83 in his book. We reproduce them here with a slight change of notations only.