bluuebunny/crossref_metadata_2025 huggingface dataset:
The Family Curriculum: Socialisation Process, Family Network and the Negotiation of Police Identities
Authors: Paes-Machado Eduardo , de Albuquerque Carlos Linhares
Published: September 2006

This article analyses how recruits' learning is filtered through their personal social network, with the aim of understanding the role of this network in police education. Based on 68 interviews with recruits about their family relationships, this analysis demonstrates that both relatives and the police academy effectively combine to groom candidates for the rank of officer in the Brazilian Military Police. Narratives from recruits about family strategies to prevent recruits from leaving the academy are analysed, demonstrating the importance of how the family both resists and adapts to its offspring's new role. For a considerable portion of lower-middle-class and non-white recruits' families, the police academy offers an important opportunity for one of its members to gain entry into the labour market. According to interviewees, the familial social network operates as a supplementary curriculum and affective background that prevents recruits from losing heart and provides them with psychological comfort in a demanding environment. For recruits, the participation of their relatives in socialisation proves to be essential to neutralising negative aspects of the police identity and learning process. We also conclude that instead of being an outcome of a dyadic or dual relationship — between the recruits and the police academy — the police habitus is also shaped by a third player represented by the recruits' familial social network, which provides recruits with a support role that the police academy and its official curriculum cannot offer.
Accident Insurance
Authors: Jean Jaime
Published: September 2006

This article examines the different types of accident insurance found in the global insurance marketplace, placing emphasis on the benefits provided and presenting a general pricing model.
Actuarial Control Cycle
Authors: Bellis Clare
Published: September 2006

The expression ‘Actuarial Control Cycle’ (ACC) is used in two ways: as a model to describe the fundamental nature of actuarial work, and as the name of a subject which since 1996 has formed Part 2 of the Australian actuarial education system. Its introduction as a subject was an important and influential educational innovation, and was the key to popularizing the ACC as a model of actuarial work. The development of the subject is recounted in this article.
Actuary
Authors: Lillevold Pål , Eyland Arne
Published: September 2006

The word ‘actuary’ derives from the Latin word ‘actuarius’, who was the business manager of the Senate of Ancient Rome. It was first applied to a mathematician of an insurance company in 1775 in the Equitable Life Insurance Society (of London, UK). By the middle of the nineteenth century, actuaries were active in life insurance, friendly societies, and pension schemes. As time has gone on, actuaries have also grown in importance in relation to general insurance, investment, health care, social security, and also in other financial applications such as banking, corporate finance, and financial engineering.

Over the times, there have been several attempts to give a concise definition of the term
actuary
. No such attempted definition has succeeded in becoming universally accepted. As a starting point, reference is made to the International Actuarial Association's description of what actuaries are:

Actuaries are multi‐skilled strategic thinkers, trained in the theory and application of mathematics, statistics, economics, probability and finance

and what they do:

Using sophisticated analytical techniques, actuaries confidently make financial sense of the short term as well as the distant future by identifying, projecting and managing a spectrum of contingent and financial risks.

This essay will adopt a descriptive approach to what actuaries are and what they do, specifically by considering the actuarial community from the following angles:

Actuarial science – the foundation upon which actuarial practice rests.

Actuarial practice.

Some characteristics of the actuarial profession.
Adjustment Coefficient
Authors: Kaas Rob
Published: September 2006

The adjustment coefficient is the number
R
appearing in the famous Lundberg upper bound: in a compound Poisson risk process with initial capital
u
 ≥ 0, the ruin probability, ψ(
u
), is bounded by e

−
Ru

. By changing the safety loading or the distribution of the individual claims that are involved in its definition, the value of
R
and with it the ruin probability can be adjusted.
Approximating the Aggregate Claims Distribution
Authors: Hardy Mary R.
Published: September 2006

In this article, we discuss approximation methods for aggregate claims distributions. The methods discussed are the normal approximation; the translated gamma approximation; Bowers' gamma approximation; the normal power approximation; Haldane's method; the Wilson–Hilferty approximation and the Esscher approximation. Worked examples are included, using a compound Poisson distribution with Pareto secondary distribution.
Audit
Authors: Coestier Bénédicte , Fombaron Nathalie
Published: September 2006

In an insurer–policyholder relation, insurees may use their informational advantage about the occurrence and/or magnitude of their losses to exaggerate the claims. Claims auditing may be a means to manage this type of insurance fraud. The economic analysis of audit has been developed in the literature principally using Costly State Verification models. After recalling the more basic results of CSV models, we discuss the major limitation of these auditing procedures, namely, the commitment assumption, and finally consider several solutions to the no‐commitment problem.
Bailey–Simon Method
Authors: Mildenhall Stephen J.
Published: September 2006

This article introduces the Bailey–Simon method for classification ratemaking and explains the connection between linear Bailey–Simon methods and generalized linear models.
Beekman's Convolution Formula
Authors: Kaas Rob
Published: September 2006

Beekman's convolution formula provides a means to compute the classical ruin probability by relating it to a compound geometric distribution.
B
ritish
A
ctuarial
J
ournal
Authors: Hart Doreen
Published: September 2006

This article shows how the
British Actuarial Journal
has evolved from previous publications of the Institute of Actuaries and the Faculty of Actuaries, and how it is still evolving. There is a description of what appears in the journal, and the structure of responsibility is outlined. There is also information on how copies of the
British Actuarial Journal
can be obtained.
Burning Cost
Authors: Mata Ana J.
Published: September 2006

The burning cost is an experience‐rating method used in reinsurance to estimate the expected loss cost in a layer. The burning cost ‘translates’ the past losses of a portfolio of policies into the prospective reinsurance period by adjusting claims for inflation and other trends.
Casualty Actuarial Society
Authors: Boa J. Michael , Underwood Alice M. , Wilkins William R.
Published: September 2006

This section addresses the formation, composition, and attributes of the Casualty Actuarial Society. In concert with and for its membership, the Casualty Actuarial Society through research and education develops and disseminates the knowledge necessary for application to the evolving exposures in today's insurance industry.
Catastrophe Derivatives
Authors: Muermann Alexander
Published: September 2006

Catastrophe derivatives are capital market instruments that allow investors outside of the insurance and reinsurance arena to invest in natural catastrophic risks. In this article, we describe the development of this market since the early 1990s, examine various stochastic models that have been proposed to model the underlying risk process, and address the pricing of these instruments.
Catastrophe Excess of Loss
Authors: Mata Ana J.
Published: September 2006

Catastrophe excess of loss is a form of nonproportional reinsurance that protects the insurance company against an accumulation of losses due to single events. The main purpose of this form of reinsurance is to protect the financial stability of the insurer and to smooth financial results between years with or without catastrophic losses.
Censored Distributions
Authors: Lawless J.F.
Published: September 2006

In some settings the exact value of a random variable is observed only if it lies within a certain range. If it lies outside this range, only that fact is known; this is referred to as censoring. This article describes censored distributions, which arise when random variables are censored. The special cases of left‐ and right‐ censoring are considered explicitly.
Censoring
Authors: Papaioannou Takis
Published: September 2006

Censoring is a process or a situation where we have partial information or incomplete observations. It is an area in statistics, engineering, and actuarial science, which has received widespread attention in the last 40 years, having been influenced by the increase in scientific computational power. The purpose of this article is to present the concept, the idea of censoring, to describe various types or kinds of censoring, and to point out its connections with survival analysis and
actuarial methods
. Censoring is closely related with censored data and is a major topic in
biostatistics
and reliability theory (life testing).
Collective Risk Models
Authors: Goovaerts Marc J.
Published: September 2006

Collective risk models model the total claims on an insurance portfolio as a compound distribution, enabling one to use recursive formulas to compute its distribution.
Competing Risks
Authors: Crowder Martin
Published: September 2006

If something can fail, it can often fail in one of several ways and sometimes in more than one way at a time. In the real world, the cause, mode, or type of failure is usually just as important as the time to failure. It is therefore remarkable that in most of the published work to date in reliability and survival analysis there is no mention of competing risks.

The study of competing risks has a respectably long history. The finger is usually pointed at Daniel Bernoulli for his work in 1760 on attempting to separate the risks of dying from smallpox and other causes. Much of the subsequent work was in the areas of demography and actuarial science. More recently, from around the middle of the last century, the main theoretical and statistical foundations began to be set out, and the process continues.
Compound Distributions
Authors: Lin X. Sheldon
Published: September 2006

In this article, compound distributions and their basic properties are discussed in an actuarial context. A brief survey of the evaluation of compound distributions is given.
Continuous Multivariate Distributions
Authors: Balakrishnan N.
Published: September 2006

In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics.
Convexity
Authors: Denuit Michel , Müller Alfred
Published: September 2006

In this article we describe the most important properties of convex sets and functions. Convexity plays an important role in many parts of actuarial sciences.
Cooperative Game Theory
Authors: Lemaire Jean
Published: September 2006

Game theory models situations of conflict and/or cooperation between economic agents. Cooperative games with transferable utilities and two‐person bargaining games, the two most important contributions of cooperative game theory to economic analysis, are reviewed and illustrated with examples.
Copulas
Authors: Carrière J.F.
Published: September 2006

This introduction starts with a short history of copulas and their role in actuarial science. Special emphasis is given to bivariate copulas, where many useful families are given. We also give general definitions and Sklar's Theorem, arguably the most important result in copulas. We finish by showing how to construct copulas. Finally, a comprehensive reference list is offered.
Counting Processes
Authors: Andersen Per Kragh
Published: September 2006

Multivariate counting processes
provide a useful mathematical framework for survival analysis or more general event history analysis.
The structure of this article is as follows. First, probabilistic properties of counting processes, useful for their applications in statistics, are reviewed. Next, counting process representations of event history data and statistical models based on counting processes are discussed and the article concludes with an example.
Coverage
Authors: Taylor Greg
Published: September 2006

This article discusses the circumstances under which a claim will be paid by an insurance policy and some basic matters affecting the amount of claim payable. Various pieces of terminology are defined.
Claims Reserving Using Credibility Methods
Authors: Verrall Richard
Published: September 2006

The background for the development of credibility theory was the situation in which there was a portfolio of similar policies, for which the natural thing would have been to use the same premium rate for all the policies. However, this would not have captured any individual differences between the policies and therefore a methodology was developed that also utilized the claims experience from the individual policy. In this way, credibility estimation can be seen to allow the pooling of information between risks in premium rating. The consequence of this is that the premium is not estimated using just the data for the risk being rated, but also using information from similar risks. In the context of claims reserving, the reason for using an approach based on credibility estimation is similar: information from different sources can be ‘shared’ in some way.

This article explains the principles of the reserving methods that use credibility theory from the actuarial literature, and refers the reader to the articles and other methods that use a similar modeling philosophy.
D
e
M
oivre,
A
braham (1667–1754)
Authors: Teugels Jozef L.
Published: September 2006

We survey the achievements in probability and actuarial sciences of one of the most prominent scientists of the eighteenth century.
D
e
P
ril Recursions and Approximations
Authors: Sundt Bjørn
Published: September 2006

In this article, we present some recursive methods for exact and approximate evaluation of aggregate claims distributions in the individual model, that is, convolutions of distributions. We discuss the exact methods of De Pril and Dhaene–Vandebroek and the approximations of De Pril, Kornya, and Hipp. For the approximations, we give error bounds.
Decrement Analysis
Authors: Pollard John
Published: September 2006

Decrement analysis intends to provide approximate values for some actuarial quantities that are not fully observable. The most common and single‐mode decrement is death and mortality rates are not fully known due to censoring of the observed lives. By using graduation methods, workable alternatives are provided. More complicated situations arise in a multiple‐decrement situation where the dependence between different causes needs to be taken into account.
Demography
Authors: Moultrie Tom A. , Dorrington Robert
Published: September 2006

Demography is the study of population dynamics (most frequently, those relating to human populations), and the measurement and analysis of associated vital rates of birth, death, migration, and marriage. Encompassing demography is a broader field of research, ‘population studies’ or ‘social demography’, which seeks to situate the results of demographic inquiries in their social, political, economic, and institutional contexts. Nevertheless, the boundaries between the two are ill‐defined. The integration of both quantitative and qualitative analysis has been essential to the discipline from its earliest origins.

There are three major aspects to demographic work: the description of a population at a point in time, by reference to specific criteria (age, sex, etc.); the analysis of the vital processes that contribute to the state of a population at that point in time; and, finally, the interpretation of the effects of these vital processes on future population dynamics, taking into account population‐specific social, economic, and cultural systems [59].

This review first traces briefly the evolution of, and trends in, demographic theory since Graunt. This article also presents the different demographic techniques in the fields of mortality, fertility, migration, and population projections.
Diffusion Approximations
Authors: Schmidli Hanspeter
Published: September 2006

Calculations of characteristics of stochastic processes, as for example, ruin probabilities, is often difficult. One therefore has to resort to approximations. Approximation of the process at a fixed point often suggests by the central limit theorem to use a normal approximation. Approximation of the whole process should then result in a Gaussian process. In many situations, the Brownian motion is the natural choice.
Diffusion Processes
Authors: Sørensen Michael
Published: September 2006

Diffusion processes form stochastic models for a number of quantities familiar within an actuarial context. Derivative pricing, volatility and interest rates are but a few examples. Moreover, many processes in actuarial science such as the surplus process, can be conveniently approximated by diffusion processes. This article explains the most important concepts needed to describe diffusion processes. It further provides a number of models that have proved their applicability within a financial context such as Brownian motion, Ornstein‐Uhlenbeck and Cox‐Ingersoll‐Ross.
Discrete Multivariate Distributions
Authors: Balakrishnan N.
Published: September 2006

In this article, we present a concise review of developments on discrete multivariate distributions. We first present some basic definitions and notations. Then, we present several important discrete multivariate distributions and list their significant properties and characteristics.
Dividends
Authors: Dickson David C.M.
Published: September 2006

In this article, we discuss risk processes modified by the inclusion of a constant dividend barrier. We give expressions for moments of the present value of dividend payments until ruin occurs, and describe strategies for setting the level of a dividend barrier. We also describe the distribution of the amount of dividends payable prior to ruin.
Early Warning Systems
Authors: Wong Johnny
Published: September 2006

An early warning system provides information to insurers for monitoring their financial stability and soundness, and to regulators for identifying those insurers who may become insolvent so that early remedial actions can be taken. It normally uses a solvency measurement system, which values the excess of assets over liabilities. A dynamic solvency measurement system, which evaluates the insurers' ability to remain solvent in the future under varying conditions, is preferred over a static solvency measurement system, which determines solvency at a particular valuation date. A good early warning system should also balance the interests of consumers, policyholders, insurers, and shareholders.
Equilibrium Theory
Authors: Citanna Alessandro
Published: September 2006

The idea of equilibrium was imported from the physical sciences into economics already in the nineteenth century [63]. Economists focused on the study of equilibrium because of the idea that this represents a rest point of an underlying dynamic system. A rest point is interpreted as a state of the economic system in which the dynamic forces governing its evolution have come to a static configuration. In economics, this static configuration has been assumed to mean essentially two things: (a) that individual economic behavior is socially consistent, that is, consumption, production, and exchange plans are feasible and can be carried out; and (b) that plans are optimal in the sense of satisfying the objectives of the individual decision makers (consumers/workers, managers, traders, and so on). The study of equilibrium was first developed in the context of markets in which each individual believes to have a negligible impact on aggregate variables such as the commodity or asset prices. These markets are called perfectly competitive, and the theory of equilibrium for perfectly competitive markets – known asWalrasian equilibrium– achieved a formal, general, and rigorous characterization in the 1950s, especially with the work of Arrow and Debreu and McKenzie. The work of Debreu and Smale established local uniqueness of equilibria, paving the way for comparative statics analysis for the Walrasian equilibrium. An alternative view would consider equilibria for an economic system in which each decision‐maker's actions have a nonnegligible impact on everyone else, and on the aggregate as well. The notion of equilibrium for these economies had been developed by Nash.
Exposure Rating
Authors: Mata Ana J.
Published: September 2006

The exposure rating method is a rating method used in reinsurance to estimate the total expected losses for the layer covered. The exposure method uses the loss experience of a similar portfolio of policies by means of a claim size distribution in order to estimate the expected losses of the portfolio of policies to be covered. This method is often used as a benchmark when there is no sufficient credible individual claim history for the specific risk.
Extremes
Authors: Beirlant Jan
Published: September 2006

The basic methods for extreme tail estimation are reviewed. More specifically, we discuss the estimation of extreme quantiles and small tail probabilities. In this, the estimation of the extreme value index is an important intermediate step. An actuarial case study is provided.
Financial Economics
Authors: Aase Knut K.
Published: September 2006

We consider a one period model of efficient risk sharing, when the set of possible sharing rules are constrained to be linear. This can be interpreted as a model of a market for common stocks. Here we study the properties of a competitive equilibrium in an incomplete market. The lack of Pareto optimality is then the typical case.

Since the marketed subspace
M
is a closed, linear subspace of
L
2
, we employ Hilbert space techniques to find the first order conditions. We also discuss conditions for the existence of an equilibrium in an incomplete market.

We conclude with a discussion of the different features of idiosyncratic risks in insurance, and risks in financial markets, where a common ground is suggested.
Financial Intermediaries: The Relationship between their Economic Functions and Actuarial Risks
Authors: Booth Philip
Published: September 2006

The purpose of this article is to explain the economic functions of financial intermediaries and financial institutions. The risks that are commonly managed by actuaries, particularly in the insurance industry, (e.g. insurance risk, market risk, interest‐rate risk etc.) arise from the economic functions of financial institutions and from the process of financial intermediation. We show that there are substantial similarities between the economic functions of nonbanks (in which actuaries have commonly managed risk) and those of banks (in which risk has generally not been managed by actuaries – at least not in the UK and US). The implication of the analysis is that risk management techniques will become closer in the banking and nonbanking sectors and that the various risk management professions and academic groups will cross the sectors.
Fire Insurance
Authors: Cassidy Paul
Published: September 2006

Fire policies cover owners of commercial or industrial property against material damage caused by fire and extraneous perils. Fire policies cover a wide range of insured properties from small rural sheds to billion dollar high‐rise buildings. Losses against these policies are dominated by large individual fire losses and other large losses caused by natural peril and manmade events that generate a large number of simultaneous claims.
Flood Risk
Authors: Younis Vicki
Published: September 2006

Exposure to flood damage is real. Various combinations of private insurance and mitigation techniques are employed to address this peril. The balance between these two methods varies considerably from one country to another. This article details the various methods presently being utilized to prevent and manage the risk of flood damage.
Fluctuation Reserves
Authors: Pentikäinen Teivo
Published: September 2006

Fluctuation reserve is a provision aimed to be a buffer against claims fluctuation and to offer means for transferring profits from advantageous years to periods of losses.
Fraud in Insurance
Authors: Guillen Montserrat
Published: September 2006

Money creates the incentive, and information asymmetries between the insured and the insurer create opportunity for insurance fraud. Here we describe the types of fraud that are currently encountered and we give some examples of insurance fraud. We discuss the difference between fraud and abuse. We present how to fight fraud with deterrence and detection. We give a brief description of the claims handling process. Several ways to control fraud are presented: specialized investigation units; statistical analysis of claims information and fraud detection methods. We show how to evaluate the performance of fraud detection models, and discuss their practical implementation.
Reinsurance, Functions and Values This is based in part on an article written by the same author and published in
Foundations of Casualty Actuarial Science, Fourth Edition
by the Casualty Actuarial Society (2001).
Authors: Patrik Gary
Published: September 2006

The functions of reinsurance vary by contract and by the relationship of the insurer and reinsurer. The functions that may be emphasized or de‐emphasized by a particular reinsurance arrangement are for the reinsurer to provide the cedant with additional underwriting capacity, to help stabilize the cedant's underwriting and financial results, to help manage the cedant's financial results and to provide management advice. The value of reinsurance is exactly parallel to that of insurance. Insurance reduces the variability of the financial costs to individuals, corporations, and other entities arising from the occurrence of specified contingent events. Reinsurance reduces the variability of the financial costs to insurance companies arising from the occurrence of specified insurance claims. Thus, its value is to further enhance innovation, competition, and efficiency in the marketplace.
Generalized Discrete Distributions
Authors: Panjer Harry H.
Published: September 2006

This article describes a number of generalized counting distributions that are used in various applications, some of them relating to insurance claim or loss counts.
G
ompertz,
B
enjamin (1779–1865)
Authors: Teugels Jozef L.
Published: September 2006

After briefly mentioning some of the highlights in the life of Gompertz, attention has been given to his importance in actuarial science. In particular, we deal with his law of mortality.
Graphical Methods
Authors: Unwin Antony
Published: September 2006

Graphical displays are excellent for giving overviews of data. It is important to distinguish between categorical and continuous data in the choice of display and to avoid including unnecessary ‘chart junk’. Recent developments include parallel coordinate plots, mosaic plots, trellis graphics, and the development of interactive graphics for exploratory analysis.
Group Life Insurance
Authors: Akselsen Einar
Published: September 2006

The article describes group life insurance and the additional benefits written in conjunction or as riders, and the requirements that might apply.
H
alley,
E
dmond (1656–1742)
Authors: Teugels Jozef L.
Published: September 2006

While Halley is best known for his astronomical work, he also contributed to actuarial science by constructing one of the first mortality and actuarial tables.
Health Insurance
Authors: Bernet Patrick M. , Getzen Thomas E.
Published: September 2006

The health insurance industry differs from most other forms of insurance in that virtually all of the insured persons expect to make claims in most years, and those at highest risk expect to have their losses subsidized by the government or other parties. In this paper, the premium pricing process is used to highlight the many special features of health insurance with particular attention to frequency of loss, post‐loss price negotiation, adverse selection, tax benefits, social insurance, IBNR and reserve policies.
History of Insurance
Authors: Sibbett Trevor
Published: September 2006

From early times, communities have looked for ways to pool resources in order to protect individuals from unexpected losses. One of the most common and long lasting arrangements, originating in the Mediterranean area and dating from before the Christian era, was a loan, with a high rate of interest, secured on the voyage of a ship, the loan being repayable only if the voyage were completed successfully. In English, this became known as bottomry, referring to the bottom of the ship.

There is evidence that the Romans practiced an early form of life insurance and bought as well as sold annuities.

In the year 1234, Pope Gregory IX banned the taking of interest and artificial contracts were developed to supplement bottomry. Following Pope Gregory's ban on bottomry, marine insurance in its basically current form developed in Florence and then in Genoa.

This article looks at insurance where a premium is paid to a third party to cover risk. Arrangements that have an element of insurance, some of which date from Babylonian times, are well covered by Trenerry and others.
Homeowners Insurance
Authors: Fry Martin
Published: September 2006

Homeowners insurance indemnifies owners against property damage arising from a number of insurable events. The insurance covers building costs and repairs, and rental costs if a property becomes uninhabitable. Factors affecting the premium for a homeowners policy are the sum insured, the construction materials of the building, the use of the building, and its location. Deductibles are often imposed.
Insurance Company
Authors: Aitken Amanda , Cohen Brett
Published: September 2006

This article defines an insurance company, describes the history of insurance companies, and discusses the environment in which modern insurance companies operate.
Integrated Tail Distribution
Authors: Lin X. Sheldon
Published: September 2006

In this article, we introduce the integrated tail distribution and its properties. Reliability classifications associated with the integrated tail distribution are discussed. We also provide a brief literature review on applications of the integrated tail distribution in actuarial science.
Interest‐Rate Modeling
Authors: Cairns Andrew J.G.
Published: September 2006

This article describes some of the main developments in interest‐rate modeling since Black & Scholes' and Merton's original articles on the pricing of equity derivatives. In particular, the article focues on continuous‐time, arbitrage‐free models for the fullterm structure of interest rates. Other models that model a limited number of key interest rates or which operate in discrete time (e.g. the Wilkie model) will be considered elsewhere.

In this article we will describe the basic principles of arbitrage‐free pricing and cover various frameworks for modeling: short‐rate models (e.g. Vasicek, Cox–Ingersoll–Ross, Hull–White); the Heath–Jarrow–Morton approach for modeling the forward‐rate curve; pricing using state‐price deflators including the Flesaker–Hughston/Potential approach; and the Markov‐functional approach.

The article works through various approaches and models in a historical sequence. Partly, this is for history's sake, but, more importantly, the older models are simpler and easier to understand. This will allow us to build up gradually to the more up‐to‐date, but more complex, modeling techniques.
Kalman Filter
Authors: Barnett Glen , Zehnwirth Ben
Published: September 2006

The Kalman Filter is an efficient method of estimation for a state space model. Best linear unbiased estimates of the mean and variance of the unknown state are updated recursively as new data is added. It is used in many areas. In actuarial work it has been mainly applied to credibility and reserving applications.
Large Deviations
Authors: Nyrhinen Harri
Published: September 2006

Large deviations theory provides insight into the probabilities of rare events by developing quantifiable estimates for them. An example is the probability for a large overshoot of the total claim amount in a portfolio. Another example is the estimation of the ruin probability starting from a very large initial capital.
Largest Claims and
ECOMOR
Reinsurance
Authors: Beirlant Jan
Published: September 2006

There exist a few intuitive and theoretically interesting reinsurance contracts that are akin to excess‐of‐loss treaties, but refer to the larger claims in a portfolio. An unlimited excess‐of‐loss contract cuts off each claim at a fixed, nonrandom retention. A variant of this principle is ECOMOR reinsurance where the priority is put at the (
r
 + 1)th largest claim so that the reinsurer pays that part of the
r
largest claims that exceed the (
r
 + 1)th largest claim. Compared to unlimited excess‐of‐loss reinsurance, ECOMOR reinsurance has an advantage that gives the reinsurer protection against unexpected claims inflation if the claim amounts increase, then the priority will also increase. A related and slightly simpler reinsurance form is largest claims reinsurance that covers the
r
largest claims but without a priority.

The article highlights some of the theoretical results that can be obtained for the case where the total volume in the portfolio is large. In spite of their conceptual appeal, largest claims type reinsurance are rarely applied in practice. The discussion hints at some of the possible reasons for this lack of popularity.
Liability Insurance
Authors: Tess Daniel
Published: September 2006

Liability insurance generally provides cover for financial loss, which arises as a result of a finding of liability under law. Many types of specialized insurance products have developed which covers certain types of liability or specific situations in which liability can arise. Some products, which are often grouped together with liability insurance do not cover liability per se, but rather cover the cost of defined benefits to injured persons in lieu of liability awards.
L
idstone,
G
eorge
J
ames (1870–1952)
Authors: Teugels Jozef L.
Published: September 2006

The contributions of Lidstone to life insurance are numerous. Even on the purely mathematical scene, he has left his mark.
Life Table
Authors: Forfar David O.
Published: September 2006

The article looks at life table functions, firstly from a probabilistic point of view and secondly from a deterministic point of view. The international notation for these functions as well as their interrelationships is shown.
Life Table Data, Combining
Authors: Tolley H. Dennis , Fellingham Gilbert W.
Published: September 2006

This article discusses methods of combining data from several life tables to form an overall life table. Combining life tables entails building a statistical model using the data from the various tables. The simplest statistical model is to assume that the probabilities of decrement for each age are the same across all tables. In this case, combining entails simple addition. When this assumption is untenable, a more complex statistical model must be built. This article illustrates how to combine life table data using a specific family of statistical models. Other candidate models for this step are mentioned at the end.
L
loyd's
Authors: Michaelson Robin
Published: September 2006

To understand Lloyd's, one has to realize what it is not. It is not an insurance company with shareholders or a mutual, nor does it accept liability for a risk as a trading entity under the name of ‘Lloyd's’. It is, in fact, a ‘society’, or group of individual and corporate members, who accept a share of a risk by operating through an underwriting syndicate, in which the individual members (called Names) are liable to the full extent of their personal private wealth, to supply the capital backup to meet the insurance liabilities, but the corporate organizations operate with a form of limited liability.
Logistic Regression Model
Authors: Dierckx Goedele
Published: September 2006

Logistic regression is a very flexible tool to study the relationship between several explanatory variables and a binary response. To fit and examine such a logistic regression model, some tools used with generalized linear models, as introduced by McCullagh and Nelder in 6, are useful. Once the model is fitted and the goodness‐of‐fit has been examined, the relationship between covariates and the response can be better understood by interpreting the coefficients in the logistic model in terms of odds ratios. The model can also be used to make predictions. As such, the logistic model provides a method to classify objects in two (or more) groups as well.
Loss Ratio
Authors: Babcock Nathan J.
Published: September 2006

Actuaries and numerous other insurance professionals use loss ratios in the measurement of profitability, the determination of appropriate pricing and reserving levels, the creation of business strategies, and the completion of financial reports. A loss ratio expresses the relationship between one of several financial items, typically insured losses, and premiums. There are many types of data from which loss ratios can be calculated. The data can include paid or incurred losses and earned or written premium; the data also can be organized by line of business, by any of several accounting period types, by insurance/reinsurance layer, or by evaluation date.
L
undberg Inequality for Ruin Probability
Authors: Yang Hailiang
Published: September 2006

This article surveys the main results and developments of Lundberg inequality for ruin probability. We briefly describe various insurance risk models in the literature, as well as the Lundberg inequality for ruin probability under these models. Finite time horizon insurance risk model and the effect of the invest income are discussed. We also mention some main results, including the Lundberg type inequality, for the severity of ruin, the distribution of surplus before ruin, and the joint distribution of surplus before and after ruin.
Lundberg,Filip (1876–1965)
Authors: Martin‐Löf Anders
Published: September 2006

Filip Lundberg (1876–1965) was a pioneer of the collective theory of risk that describes the surplus of, for example, a branch of an insurance company as a stochastic process. The purpose of the theory is to study the probability distribution of the surplus and of the time until ruin.
Market Equilibrium
Authors: Courbage Christophe
Published: September 2006

Different ways of modeling market equilibrium have been used in economic literature. This paper briefly reviews these models as well as their limitations and extensions. In particular, the Arrow–Debreu model, the CAPM and the insurance CAPM are presented.
M
arkov Chains and
M
arkov Processes
Authors: Jacobsen Martin
Published: September 2006

In many applications, the usual assumption of independent and identically distributed random variables has to be abandoned. Markov dependence is a first possibility. We deal with Markov chains in discrete and continuous time. We then extend the setting to Markov processes on more general state spaces. We pay special attention to stationary processes and to piecewise deterministic Markov processes where the behavior of the process between jumps is basically deterministic.
Mixed Poisson Distributions
Authors: Panjer Harry H.
Published: September 2006

This article describes some properties of mixed Poisson distributions, as they represent distributions of the number of insurance claims or losses.
Dynamic Financial Modeling of an Insurance Enterprise
Authors: Hardy Mary R.
Published: September 2006

A dynamic financial insurance model is an integrated model of the assets and liabilities of an insurer. In the United Kingdom, these models may be called ‘model offices’. Modeling the insurer as a whole entity differs from individual policy or portfolio approaches to modeling in that it allows for interactions and correlations between portfolios, as well as incorporating the effect on the organization of decisions and strategies, which depend on the performance of the insurer as a whole. For example, profit distribution is most sensibly determined after consideration of the results from the different insurance portfolios that comprise the company, rather than at the individual portfolio level. The insurance enterprise model takes a holistic approach to asset–liability modeling, enabling synergies such as economies of scale, and whole insurer operations to be incorporated in the modeling process.
Multivariate Statistics
Authors: Jensen Uwe
Published: September 2006

After a summary of the most essential fundamentals on multivariate random variables and their distributions as well as estimation and testing in multivariate statistics, five important multivariate techniques are introduced: principal components analysis (PCA), factor analysis, multivariate analysis of variance (MANOVA), discriminant analysis and cluster analysis.
Nonexpected Utility Theory
Authors: Machina Mark J.
Published: September 2006

Although the expected utility model of risk preferences has long been the most widely used model of choice under uncertainty, a growing body of evidence has uncovered systematic departures from expected utility maximization. Researchers have characterized the form of these departures, developed several models of nonexpected utility risk preferences, and have applied these models to the analysis of standard questions such as the theory of insurance.
Operations Research
Authors: Bäuerle Nicole
Published: September 2006

In this section, we present the most important optimization problems arising in deterministic operations research and give a concise survey of common solution techniques. More precisely, we consider linear programming, combinatorial optimization, integer programming, nonlinear programming, and dynamic programming. Typical problems in these areas are also mentioned.
Participating Business
Authors: O'Brien Christopher David
Published: September 2006

In participating life business, also referred to as ‘with profits’, there are policyholders with rights to share in the surplus (or profits) of the business. This means there are important issues in the management of such business, including how to price policies that contain such rights, how to determine the investments of the fund (given that the obligations to policyholders depend on the surplus that is earned), and how to assess the amount of surplus to be distributed. There is then the question of how to share surplus between the participating policyholders and, in a stock life insurer, the shareholders.
Pension Fund Mathematics
Authors: Cairns Andrew J. G.
Published: September 2006

This article reviews the role of mathematics as a tool in the running of pension funds. It considers separately defined benefit (DB) and defined contribution (DC) pension funds.
Pensions: Finance, Risk and Accounting
Authors: MacNicol Roger
Published: September 2006

This article deals with the financing of defined benefit pension schemes. The financing of defined contribution schemes is much simpler and can be summarized as follows. An amount is paid into a scheme for each member. That amount will be determined by market forces (what other companies, competing for the same workers, are paying) and by what a company can afford. Where specific benefit targets are used within defined contribution schemes, they take on some of the characteristics of defined benefit arrangements and their financing will follow, to a greater or lesser extent (depending on the type of benefit guarantee given) the principles below.

Defined benefit pensions can be financed in a number of ways. At one extreme, ‘Pay As You Go’ (PAYG) systems do not involve any prefunding (i.e. the accumulation of funds during employees' working lifetimes) whatsoever. At the other extreme, an immediate lump sum might be set aside, its amount being sufficient (on an appropriate set of actuarial assumptions) to meet all future pension outgo. This approach is very unlikely to be used in practice.
Pensions
Authors: MacNicol Roger
Published: September 2006

Pension schemes are normally constructed from different sources: provisions offered by the state, mandatory employer plans, voluntary employer plans and personal savings. The article illustrates these ingredients with pension plans as they exist in a number of different countries, such as the USA, UK, Germany, Japan and France.
Phase‐Type Distributions
Authors: Drekic Steve
Published: September 2006

This article summarizes some of the key distributional properties associated with phase‐type distributions, which are used extensively in many areas of applied probability, namely, queueing theory and insurance ruin theory (
see
).
Poisson Processes
Authors: Grandell Jan
Published: September 2006

For a long time, Poisson processes have formed the most popular stochastic model for claim arrivals in an insurance portfolio. No wonder that in the course of time a wealth of generalizations have been constructed such as point processes, Cox processes and mixed Poisson processes. The essential ingredients of these processes are included.
Policy
Authors: Aitken Amanda , Forker Arlene
Published: September 2006

This article defines an insurance policy and sets out some of the standard features of a policy document or contract.
Pooling of Employee Benefits
Authors: Ott Martin
Published: September 2006

This article explains the basic concept of multinational pooling of employee benefits and the various forms of risk sharing. It highlights the impact of risk retention on the result after pooling, as well as other aspects that are crucial for the profitability of pooled business.
Premium Principles
Authors: Young Virginia R.
Published: September 2006

In this review article, we discuss how premium principles arise in theory and in practice. We propose three methods that actuaries use to derive premium principles: (1) thead hoc methodin which the actuary simply proposes a (potentially) reasonable premium principle then studies its properties; (2) thecharacterization methodin which the actuary lists the properties that she wants the premium principle to satisfy, then finds (all) the premium principles that satisfy those properties; and (3) theeconomic methodin which the actuary espouses an economic theory and determines the resulting premium principle. These methods are not exclusive, as we note in the article.
Proportional Reinsurance
Authors: Dickson David C.M.
Published: September 2006

Proportional reinsurance is described in this article.
Random Number Generation and Quasi‐MonteCarlo
Authors: L'Ecuyer Pierre
Published: September 2006

Probability theory defines random variables and stochastic processes in terms ofprobability spaces, a purely abstract notion whose concrete and exact realization on a computer is far from obvious. (Pseudo) random number generators (RNGs) implemented on computers are actually deterministic programs, whichimitateto some extent, independent random variables uniformly distributed over the interval [0,1] (i.i.d.U[0,1], for short). RNGs are a key ingredient for Monte Carlo simulations, probabilistic algorithms, computer games, cryptography, casino machines, and so on.