bluuebunny/crossref_metadata_2025 huggingface dataset:
Pension Fund Mathematics
Authors: G. Cairns Andrew J.
Published: September 2014

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 2014

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 2014

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.
Present Values and Accumulations
Authors: Macdonald Angus S.
Published: September 2014

Money has a
time value
; if we invest $1 today, we expect to get back more than $1 at some future time as a reward for lending our money to someone else who will use it productively. Suppose that we invest $1, and a year later we get back $(1 +
i
). The amount invested is called the
principal
, and we say that
i
is the
effective rate of interest per year
. Evidently, this definition depends on the time unit we choose to use. In a riskless world, which may be well approximated by the market for good quality government bonds,
i
will be certain, but if the investment is risky,
i
is uncertain, and our expectation at the outset to receive $(1 +
i
) can only be in the probabilistic sense.

We can regard the accumulation of invested money in either a retrospective or prospective way. We may take a given amount, $
X
say, to be invested now and ask, as above, to what amount will it accumulate after
T
years? Or, we may take a given amount, $
Y
say, required in
T
years' time (to meet some liability perhaps) and ask, how much we should invest now, so that the accumulation in
T
years' time will equal $
Y
? The latter quantity is called the
present value
of $
Y
in
T
years' time. For example, if the effective annual rate of interest is
i
per year, then we need to invest $1/(1 +
i
) now, in order to receive $1 at the end of one year. In standard actuarial notation, $1/(1 +
i
) is denoted
v
, and is called the discount factor. It is immediately clear that in a deterministic setting, accumulating and taking present values are inverse operations.
Profit Testing
Authors: Richards Stephen
Published: September 2014

Every business needs to know if its products are profitable. However, it is much harder to determine the profitability of long‐term life and pensions business than most other industries. Strictly speaking, one only knows if a tranche of business has been profitable when the last contract has gone off the books, which could take fifty years for certain kinds of contract. Clearly, some methodology is needed to assess likely profitability before writing the business in the first place. This article is devoted to the subject of profit testing, the process of assessing the profitability of an insurance contract in advance of it being written.
Risk‐Based Capital Requirements
Authors: Brender Allan
Published: September 2014

An insurer needs sufficient financial resources to survive an unfavorable experience, pay all policyholder claims and continue business. For a company, this capital might be different from that required by supervisors or regulators. We survey the major components needed in the construction of the capital requirements. An illustration from the NAIC‐requirements in the US is given.
Surplus in Life and Pension Insurance
Authors: David O'Brien Christopher
Published: September 2014

Surplus in life insurance is a key issue for participating business: actuarial control over the emergence and distribution of surplus is a major subject in the management of life insurance companies. Although we here concentrate on surplus in the context of participating life business, surplus is also relevant in any kind of fund in which long‐term liabilities may be valued on the basis of assumptions about the future. For example, shareholders have needs and expectations of surplus in nonparticipating life business, with premium rates and payouts being determined with a view to rewarding shareholders, who have provided capital and run risks. In pensions business there are similar issues concerning the sources, size, analysis, and uses of surplus.
Unit‐Linked Business
Authors: Richards Stephen
Published: September 2014

This article is about unit‐linked insurance business, including unitised with‐profits (UWP) business. The major distinguishing feature of unit‐linked business is that a separate and explicit asset account is maintained for each policy. Each policy can therefore be invested entirely independently of the others, and this investment flexibility is under the control of the policyholder, not the insurer. The value of a unit‐linked policy is directly linked to the investment performance of the unitised funds selected by the policyholder. Unlike traditional with‐profits business, there is no element of discretion for setting bonuses for pure unit‐linked business. An important consequence of this for the insurer is that expenses and charges are explicitly separated, and the simple ‘cost‐plus’ approach to managing pricing has to be abandoned in favor of profit testing.
B
ayesian Claims Reserving
Authors: Alba Enrique
Published: September 2014

Claims reserving methods are usually classified as stochastic or nonstochastic (deterministic) depending on whether or not they allow for random variation. Bayesian methods fall within the first class. Being stochastic, they allow the actuary to carry out statistical inference of reserve estimates as opposed to deterministic models, like the traditional chain‐ladder. As an inference process, the Bayesian approach is an alternative to classical or frequentist statistical inference. From a theoretical point of view, Bayesian methods have an axiomatic foundation and are derived from first principles. From a practical perspective, Bayesian inference is the process of fitting a probability model to a set of data and summarizing the result by a probability distribution on the parameters of the model and on unobserved quantities, such as predictions for new observations.
Claims Reserving Using Credibility Methods
Authors: Verrall Richard
Published: September 2014

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.
Random Number Generation and Quasi‐MonteCarlo
Authors: L'Ecuyer Pierre
Published: September 2014

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.
Numerical Algorithms
Authors: Horebeek Johan
Published: September 2014

We give an overview of several computer intensive numerical algorithms that have special relevance in applications with an intrinsic stochastic component.
Simulation Methods for Stochastic Differential Equations
Authors: Platen Eckhard
Published: September 2014

As we try to build more realistic models in risk management, the stochastic effects need to be carefully taken into account and quantified. This paper provides a very basic overview on simulation methods for stochastic differential equations (SDEs).
Copulas: Examples and Construction
Authors: Carrière J.F.
Published: September 2014

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.
Failure Rate
Authors: Cai Jun
Published: September 2014

In this article, we survey the properties of the failure rate function and issues in insurance related to the failure rate.
Integrated Tail Distribution
Authors: Lin X. Sheldon
Published: September 2014

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.
Mean Residual Lifetime
Authors: Cai Jun
Published: September 2014

This article reviews the properties of the mean residual lifetime of a distribution and considers the applications of mean residual lifetimes in insurance, finance, and reliability.
Actuary
Authors: Lillevold Pål , Eyland Arne
Published: September 2014

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.
Convexity
Authors: Denuit Michel , Müller Alfred
Published: September 2014

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.
Transforms
Authors: Grübel Rudolf
Published: September 2014

The use of transforms is one of the pervasive ideas in mathematics and the sciences. From a pragmatic point of view, a transformation can be regarded as a tool for simplifying an otherwise difficult operation, for example, a differential equation can be turned into a simple algebraic equation with the help of Laplace transforms. Even the formula, log(x·y) = logx + logy, in connection with the traditional use of logarithmic tables and slide rules may be seen in this light. Transforming an object may also provide insight into its structure, for example, writing a periodic function as a superposition of sine waves. From a theoretical point of view, transforms of the type considered in this article are at the core of major mathematical theories such as harmonic analysis; they have initiated research that spans the whole range of contemporary mathematics.
Censored Distributions
Authors: Lawless J.F.
Published: September 2014

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.
Convolutions of Distributions
Authors: Cai Jun
Published: September 2014

This article reviews the properties of convolutions of distributions and considers probability models in insurance that are related to the convolutions.
Discretization of Distributions
Authors: Panjer Harry H.
Published: September 2014

This article describes some simple methods for discretizing a distribution on a uniform span. It is necessary to discretize the severity (loss amount) distribution in order to implement recursive methods for computing the aggregate claims (or loss) distribution.
Extreme Value Distributions
Authors: Beirlant Jan
Published: September 2014

Extreme value distributions arise as nondegenerate limits of sequences of maxima from pure random samples. The generalized extreme value distribution encompasses all such limiting distributions. We review the estimation of parameters for this model and discuss actuarial applications.
Generalized Discrete Distributions
Authors: Panjer Harry H.
Published: September 2014

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.
Mixed Poisson Distributions
Authors: Panjer Harry H.
Published: September 2014

This article describes some properties of mixed Poisson distributions, as they represent distributions of the number of insurance claims or losses.
Mixtures of Exponential Distributions
Authors: Cai Jun
Published: September 2014

This articles discusses the properties mixed exponential distributions and consider their examples and variations appearing often in insurance.
Truncated Distributions
Authors: Lawless J. F.
Published: September 2014

A probability distribution for a random variable
X
is said to be truncated when some set of values in the range of
X
is excluded. This article describes truncated distributions and explicitly discusses the special cases of left truncation and right truncation.
Dodson, James (1710‐1757)
Authors: Teugels Jozef L.
Published: September 2014

Dodson has been crucial in the foundation of the first life insurance company based on scientific principle.
Gompertz, Benjamin (1779‐1865)
Authors: Teugels Jozef L.
Published: September 2014

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.
Huygens, Christiaan and Lodewijck (1629‐1695)
Authors: Teugels Jozef L.
Published: September 2014

Christiaan and Lodewijck Huygens played a role in the early development of probability theory and its application to insurance topics.
Price, Richard (1723‐1791)
Authors: Teugels Jozef L.
Published: September 2014

Price was a great thinker from the second half of the eighteenth century. Apart from contributions to philosophy, religion, and politics, he produced a number of substantial publications on both theoretical and practical aspects of life insurance.
Redington, Frank Mitchell (1906‐1984)
Authors: Teugels Jozef L.
Published: September 2014

Redington has been considered one of the most influential members of the actuarial community, especially for his theory of immunization.
Information Criteria
Authors: Claeskens Gerda
Published: September 2014

The selection of an adequate model is central to any data analysis. Information criteria provide formalized ways of model selection.
Maximum Likelihood
Authors: Duan Jin‐Chuan , Fulop Andras
Published: September 2014

We describe the maximum likelihood (ML) estimation and inference. Main theoretical results under the i.i.d. assumption are presented along with discussions. To demonstrate the ML inference, an example dealing with large medical claims and their determining characteristics is presented. We then turn to the ML estimation for stationary dynamic models (i.e. dependent data points) and introduce the quasi‐ML principle as a way of dealing with potential distributional misspecification. The US interest rate series is used to illustrate the quasi‐ML inference for dependent data.
Outlier Detection
Authors: Gather Ursula , Pawlitschko Jörg
Published: September 2014

The analysis of all kinds of statistical data usually includes the detection of outliers as a first exploratory step. The reason for this is twofold: on the one hand we want to screen for aberrant values firstly and on the other hand we are interested in identifying data points that are of special interest. This paper discusses methods of detecting outliers in statistical data for a couple of often‐arising data structures. It also aims at clarifying the notion of an outlier, which often is only vaguely described in the literature.
Frailty
Authors: Hougaard Philip
Published: September 2014

A frailty model is a random effects model for survival data or other time‐to‐event data. Conceptually, frailty models are similar to the normal distribution mixed models, but they are dedicated to the survival data case, where observations may be censored and where updating is natural as the events happen over time. In actuarial science this covers both life/pension for married couples, and repeated events, like car accidents. The frailty is the common random term and is assumed to enter multiplicatively in the hazard function. The gamma distribution is the most commonly used for the frailty, but other distributions may also be useful. Over the last 20 years, both theory and applications have developed so that by now the frailty models have almost become standard models.
Compound Process
Authors: Cai Jun
Published: September 2014

In this article, we review the properties of compound Poisson processes and consider the generalizations of compound Poisson processes. Further, we discuss topics such as the limit laws of compound processes, the approximations to the distributions of compound processes, and the asymptotic behaviors of the tails of compound processes.
Gaussian Process: Overview
Authors: Débicki Krzysztof
Published: September 2014

The class ofGaussian stochastic processesplays an important role in stochastic modeling and is widely used as a rich source of models in many areas of applied probability, including actuarial and financial mathematics.

There are many practical and theoretical reasons for using Gaussian processes to model actuarial problems. For instance, the family of Gaussian processes covers a large class of correlation structures and enables explicit analysis of models for which classical renewal‐type tools do not work.

On the other hand, theoretical results, mostly based on central limit theorem‐type argumentation, formally justify the use of Gaussian processes.
M
arkov Chains and
M
arkov Processes
Authors: Jacobsen Martin
Published: September 2014

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.
Queueing Theory: Further Observations
Authors: Sigman Karl
Published: September 2014

The mathematical theory of congestion is associated with delays while waiting in a line or
queue
for service in a
system
. Examples of such systems include banks, post offices, and supermarkets as well as telecommunication systems involving telephones, computer networks, the Internet/the World Wide Web, inventory, and manufacturing processes. The early development of the field was motivated by telephone systems and the ways in which they could be made to operate more efficiently.

Much of the theory relies heavily on the use of
probability theory
and
stochastic processes
, and as such is widely viewed as a subfield of stochastic modeling and applied probability. There is also significant interplay with other fields such as scheduling theory, inventory theory, and insurance risk theory; it is a central part of
operations research
.
Renewal Theory
Authors: Willmot Gordon E.
Published: September 2014

Any sequence of positive, independent and identically distributed random variables can be considered as a renewal process. Traditional examples are the interclaim times and the successive claims in a homogeneous portfolio. The article describes the most important quantities and results from renewal theory. Also defective, delayed and discrete‐type renewal processes are discussed and illustrated with examples from actuarial science.
Nonparametric Statistics
Authors: Brazauskas Vytaras
Published: September 2014

The intent of this article is to give a brief overview of nonparametric statistical methods. We first describe the most commonly used nonparametric procedures in standard statistical settings involving one, two, or more samples. Then we turn to more specialized topics, such asempirical estimation,resampling methods, andsmoothing techniques, which find frequent application in actuarial research and practice. In each case, the emphasis is on the description of the problem and a particular standard approach to its solution, rather than attempting to review all existing procedures that are available for the problem. Also, for each topic, a list of references that treat applications of these methods to actuarial problems is provided.
Coupling
Authors: Thorisson Hermann
Published: September 2014

Coupling is a probabilistic tool that links two random variables (or stochastic processes) in such a way that their properties become similar, sometimes even identical. Important and readily proved properties of one of the components are then transmitted to a less accessible second component.
HiddenMarkov Models
Authors: Rydén Tobias
Published: September 2014

The outcomes of a stochastic process are often influenced by another, not fully observable process. For example, a financial time series depends on the hidden state of the market. In most cases, this hidden process is taken to be a Markov chain. We investigate the probabilistic modelling of such processes and the resulting statistical procedures.
Large Deviations
Authors: Nyrhinen Harri
Published: September 2014

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.
Phase Method
Authors: Bladt Mogens
Published: September 2014

The method of stages (due to Erlang) refers to the assumption of – and techniques related to – a positive random variable
X
, which can be decomposed into (a possibly random number of) stages each of which having an exponentially distributed duration.
Stability
Authors: Rusaityte Deimante
Published: September 2014

We discuss the stability problem for stochastic models. The general stability concept was introduced by Zolotarev. Its basic statements with a view towards actuarial risk theory were reproduced by Kalashnikov. Particular attention is payed to the stability of the ruin probability. We provide two examples of stability bounds: for finite state Markov chains and the ruin probability in the Sparre Andersen risk model.
Stochastic Control Theory
Authors: Højgaard Bjarne
Published: September 2014

The theory of stochastic control deals with the problem of optimizing the behavior of stochastic processes in a dynamic way, which means that the controller at any given point in time can make new decisions based on all information, which is available to him at that time.
Resampling
Authors: Verrall Richard
Published: September 2014

Resampling methods have become popular in statistics because of the advance in computer power. They can be used to simplify many of the commonly used statistical procedures. In actuarial science, they are particularly relevant to the increasing use of stochastic and Simulation of stochastic processes simulation‐based techniques and it is likely that their use will increase further. We give an introduction to resampling methods, in particular, bootstrapping, and provide some examples of their use in practice.
Cohort
Authors: Eben Kryštof , Malý Marek
Published: September 2014

A cohort is a group of subjects, identified by a common characteristic, which is studied over a period of time with respect to an outcome – event of interest. The defining characteristic is often year of birth. The event of interest may be death or disease onset or generally any event that possesses a well‐defined intensity of occurrence.

In actuarial science, purchase of a life or medical insurance policy may play the role of defining characteristic – death or insurance claim is the event of interest in this case. On the other hand, marketing of insurance products may require a study of birth cohorts with respect to purchasing life or medical insurance. Here, obviously the purchase is the event of interest.
Life Table Data, Combining
Authors: Tolley H. Dennis , Fellingham Gilbert W.
Published: September 2014

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.
Accounting
Authors: Blanchard Ralph
Published: September 2014

This article's purpose is to give an overview of accounting concepts and issues relevant to the actuary. To do this, it is divided into the following sections:

Purpose of accounting

Types of accounting

Principal financial statements

Sources of accounting rules

Selected accounting concepts

Common accounts for insurance companies.
Annual Statements
Authors: Babcock Nathan J.
Published: September 2014

Insurance companies and other business organizations that engage in the business of insuring or reinsuring property–casualty exposures are usually required to file
Annual Statements
with the governmental agencies that regulate insurance operations in the pertinent geographic region. These Annual Statements are detailed financial documents that provide information that are not typically available in a company's annual report (such as is provided to stockholders, for example). However, Annual Statements are generally available to interested members of the public, as they are documents in the public record.
Deductible
Authors: Buchanan Robert , Priest Colin
Published: September 2014

This article explains the operation of deductibles and franchises.
Flood Risk
Authors: Younis Vicki
Published: September 2014

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.
Insurance Company
Authors: Aitken Amanda , Cohen Brett
Published: September 2014

This article defines an insurance company, describes the history of insurance companies, and discusses the environment in which modern insurance companies operate.
Liability Insurance
Authors: Tess Daniel
Published: September 2014

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.
Loss‐of‐Profits Insurance
Authors: Fry Martin
Published: September 2014

Loss‐of‐Profits insurance is intended to cover losses to a business following physical damage by fire or breakdown, until turnover has recovered to a similar level to that prior to the damage. It requires that a fire or machinery breakdown policy has been effected by the insured. Cover is for a maximum sum insured representing the insured's gross profit and the increased cost of working for the anticipated period that production is interrupted following the physical damage, and for a maximum indemnity period representing the anticipated period to restore the business to normal operations and profitability.
Mutuals
Authors: Szuch William
Published: September 2014

This article outlines the concept of mutuality that comes from friendly societies, life companies, and general insurance. Reference is also made to mutuality in other facets of society and community structure.
Non‐Life Insurance
Authors: Taylor Greg
Published: September 2014

The following items of terminology are equivalent: non‐life insurance, property–liability insurance, property and casualty insurance, and general insurance.

Non‐Life insurance is defined and distinguished from other forms of insurance. Classes of non‐life insurance are defined and discussed. Reinsurance is also defined.
Policy
Authors: Aitken Amanda , Forker Arlene
Published: September 2014

This article defines an insurance policy and sets out some of the standard features of a policy document or contract.
Self‐Insurance
Authors: Wade Roger
Published: September 2014

A description of various types of self‐insurance and the actuarial processes frequently associated with self‐insured programs.
Insolvency
Authors: David Cummins J.
Published: September 2014

The objective of insurance is to provide risk pooling and diversification for individuals and business firms facing the risk of loss of life or property due to contingent events. Each individual unit insured through an insurance enterprise pays a premium to the insurer in return for the promise that those individuals suffering a defined loss event during the coverage period will be compensated for the loss by the insurance company. Some period of time elapses between the date of issuance of the insurance contract and the payment of losses to claimants against the pool. This can be anywhere from a few weeks, as in the case of short‐term property insurance policies, to a period of years or decades, as in the case of long‐tail liability insurance policies, life insurance, and annuities. The insurance company holds the funds generated by collecting and investing premiums to finance the claim payments that are eventually made against the pool. Because losses can be larger than expected, insurance companies hold equity capital over and above the expected value of future claim costs in order to ensure policyholders that claims will be paid in the event of adverse deviations. Nevertheless, there is a significant risk that the funds held by the insurer will be inadequate to pay claims. This is the risk of insolvency or bankruptcy, which provides the primary rationale for the intense regulation of insurance companies worldwide.
Lotteries
Authors: Pflug Georg
Published: September 2014

Lottery companies sell risk to customers. They are natural counterparts to insurance companies who buy risk from customers. Insurance contracts contain a positive risk premium, that is, the asked premium exceeds the expected losses to cover the administrative costs and to allow profit and a safety margin for the insurance company. Lottery contracts contain a negative risk premium, that is, the price of the lottery ticket exceeds the expected win, again to allow a profit for the lottery company or – in state‐owned lotteries – for the national finances.

It seems quite paradoxical that a person may hold some insurance contracts (thus seems to be risk‐averse) and at the same time buy lottery tickets (thus seem to be risk‐seeking). A preliminary explanation can be found in the nature of the two risks: While insurance protects against unwanted risks and risks that cannot be controlled (accident, fire, etc.), lotteries offer new, independent, maybe even thrilling risks.
Market Equilibrium
Authors: Courbage Christophe
Published: September 2014

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.
Nonexpected Utility Theory
Authors: Machina Mark J.
Published: September 2014

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.
Oligopoly in Insurance Markets
Authors: Sonnenholzner Michael , Wambach Achim
Published: September 2014

Although empirical evidence on oligopolistic behavior in some sectors of the insurance industry exists, relatively few theoretical models have been developed. We discuss the cause for this discrepancy, elaborate on the classical oligopoly models and their applicability to the insurance market, and introduce the few models that are specific to the insurance industry. The underlying mechanism in these models is that undercutting a rival makes the pool of risks unattractive and thus, oligopolistic market power can be sustained.
Risk Utility Ranking
Authors: J. Goovaerts Marc , Kaas Rob
Published: September 2014

Two theories to explain why insureds are willing to pay more than the expected loss as an insurance premium are the expected utility hypothesis and Yaari's dual theory of choice under risk.
Capital Allocation for
P
&
C
Insurers: A Survey of Methods
Authors: Venter Gary G.
Published: September 2014

Capital allocation is never an end in itself, but rather an intermediate step in a decision‐making process. Trying to determine which business units are most profitable relative to the risk they bear is a typical example. Pricing for risk is another.

While the general topic is capital allocation, this article looks at methods of answering the questions that capital allocation addresses. The following four basic approaches will be reviewed:

Selecting a risk measure and an allocation method, and using them to allocate all capital.

Comparing the actual versus model pricing by a business unit.

Computing the cost of the marginal capital needed for or released by target strategies.

Evaluating the profitability in comparison to a leveraged mutual fund.
Credit Risk
Authors: Gielens Geert
Published: September 2014

In this article, we present a brief overview of the most important aspects of credit risk and the way it is treated in financial markets. More specifically, we briefly cover subjects such as default probabilities, loss given default, credit default swaps, and collateralized debt obligations.
DFA‐Dynamic Financial Analysis
Authors: Blum Peter , Dacorogna Michel
Published: September 2014

Dynamic Financial Analysis (‘DFA’) is a systematic approach based on large‐scale computer simulations for the integrated financial modeling of non‐life insurance and reinsurance companies aimed at assessing the risks and the benefits associated with strategic decisions.

The most important characteristic of DFA is that it takes an integrated, holistic point of view, contrary to classic financial or actuarial analysis in which different aspects of one company were considered in isolation from each other. Specifically, DFA models the reactions of the company in response to a large number of interrelated risk factors including both underwriting risks – usually from several different lines of business, as well as asset risks. In order to account for the long time horizons that are typical in insurance and reinsurance, DFA allows dynamic projections to be made for several time periods into the future, where one time period is usually one year, sometimes also one quarter. DFA models normally reflect the full financial structure of the modeled company, including the impact of accounting and tax structures. Thus, DFA allows projections to be made for the balance sheet and for the profit‐and‐loss account (‘P&L’) of the company. Technically, DFA is a platform using various models and techniques from finance and actuarial science by integrating them into one multivariate dynamic simulation model. Given the complexity and the long time horizons of such a model, it is not anymore possible to make analytical evaluations. Therefore, DFA is based on stochastic simulation (also called Monte Carlo imulation), where large numbers of random scenarios are generated, the reaction of the company on each one of the scenarios is evaluated, and the resulting outcomes are then analyzed statistically.
Foreign Exchange Risk in Insurance
Authors: Chan Ngai Hang
Published: September 2014

This note aims at providing an overview of foreign exchange risk related to actuarial science. After reviewing basic concepts of foreign exchange risk and related financial theory and risk management techniques, references to actuarial studies are provided.
Financial Intermediaries: The Relationship between their Economic Functions and Actuarial Risks
Authors: Booth Philip
Published: September 2014

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.
Financial Markets
Authors: Nitzsche Dirk
Published: September 2014

Financial markets provide the antithesis of Polonius' advice to his son in Shakespeare's
Hamlet
, of ‘neither a borrower or lender be’. Individuals benefit not only from consuming goods and services that are primarily produced by firms but also by the government sector (e.g. education, health, and transport facilities in many countries). To produce ‘goods’, firms and the government often have to finance additional current and capital investment expenditures by borrowing funds. Financial markets and institutions facilitate the flow of funds between surplus and deficit units.
Market Models
Authors: Pelsser Antoon
Published: September 2014

Interest rate modelling is one of the crucial ingredients in the calculation of the market value of insurance products. The standard case is the LIBOR Market Model where all interest rates have log‐normal distributions. We deal with LIBOR rates and options on LIBOR rates (caplets and floorlets) first, then with swap rates and options on swap rates (swaptions).
Derivative Pricing, Numerical Methods
Authors: Vetzal K.R.
Published: September 2014

Numerical methods are needed for derivatives pricing in cases where analytic solutions are either unavailable or not easily computable.

The subject of numerical methods in the area of derivatives valuation and hedging is very broad. A wide range of different types of contracts are available, and in many cases there are several candidate models for the stochastic evolution of the underlying state variables. Many subtle numerical issues can arise in various contexts. A complete description of these would be very lengthy, so in this article we will only give a sample of the issues involved.

The article first presents a detailed description of the different methods available in the context of the Black – Scholes – Merton model for simple European and American‐style equity options. It then describes how the methods can be adapted to more general contexts, such as derivatives dependent on more than one underlying factor, path‐dependent derivatives, and derivatives with discontinuous payoff functions.
Risk‐Based Capital Allocation
Authors: Albrecht Peter
Published: September 2014

This contribution is intended to serve as a survey of techniques of risk‐based capital allocation. Before going into technical detail, however, some words have to be spent on the conceptions of risk‐based capital and capital allocation.
Risk Measures
Authors: Albrecht Peter
Published: September 2014

The literature on risk is vast (the academic disciplines involved are, for instance, investment and finance, economics, operations research, management science, decision theory, and psychology). So is the literature on risk measures. This contribution concentrates on financial risks and on financial risk measures (this excludes the literature on perceived risk (the risk of lotteries perceived by subjects) the literature dealing with the psychology of risk judgments and also the literature on inequality measurement.
Bonus‐Malus Systems
Authors: Lemaire Jean
Published: September 2014

Bonus‐malus is the most common form of a posteriori rating in automobile third‐party liability insurance. The policyholder moves around the classes of a Markov chain according to his annual number of claims. Claim‐free years are rewarded by premium discounts or bonuses; at‐fault accidents are penalized by surcharges called maluses. The different principles underlying the design and evaluation of bonus‐malus systems are reviewed.
Catastrophe Models and Catastrophe Loads
Authors: Meyers Glenn
Published: September 2014

Natural catastrophes such as earthquakes, hurricanes, tornadoes, and floods have an impact on many insurers, and the accumulation of losses to an insurer can jeopardize the financial well‐being of an otherwise stable, profitable insurer. Hurricane Andrew, in addition to causing more than $16 billion in insured damage, left at least 11 companies insolvent in 1992. The 1994 Northridge earthquake caused more than $12 billion in insured damage in less than 60 seconds.

Fortunately, such events are infrequent. But it is exactly their infrequency that makes the estimation of losses from future catastrophes so difficult. The scarcity of historical loss data makes standard actuarial techniques of loss estimation inappropriate for quantifying catastrophe losses. Furthermore, the usefulness of the loss data that does exist is limited because of the constantly changing landscape of insured properties.

It is these two aspects of catastrophic losses – the possibility that a quick accumulation of losses can jeopardize the financial well‐being of an insurer, and the fact that historical loss information provides little help in estimating future losses – that this article addresses.
Credibility Theory
Authors: Norberg Ragnar
Published: September 2014

This survey of actuarial credibility theory traces its origins, describes its evolutionary history, gives an account of its main issues and results, and assesses its merits with a view to related work in statistical science.
Ordering of Risks
Authors: Kaas Rob
Published: September 2014

The theory of Ordering of Risks has many actuarial applications, and is in fact one of the most important items in the actuarial toolkit. The most important concept is
stop‐loss order
, which compares risks as to their variability.
Ratemaking
Authors: McClenahan Charles L.
Published: September 2014

The goal of the ratemaking process is the establishment of actuarially sound rates for property and casualty insurance, or other risk transfer mechanisms. Because ratemaking generally requires that rates be established prior to the inception of the insurance, a rate is ‘an estimate of the expected value of future costs’. Such rates are actuarially sound if they provide for all of the expected costs of the risk transfer and appropriately reflect identified individual risk characteristics.

Many state rating laws in the United States require that insurance rates be ‘not inadequate, excessive or unfairly discriminatory’. If a rate is actuarially sound, it is deemed to meet these regulatory requirements without regard to the extent to which the actuarial expectations are consistent with the actual developed experience.

This article will introduce and discuss the basic elements of property and casualty actuarial ratemaking. The examples and illustrations have been substantially simplified, and it should be noted that the methods presented herein are but a few of the methods available and may not be appropriate for specific actuarial applications.
Alternative Risk Transfer
Authors: Neuhaus Walther
Published: September 2014

This paper gives a summary of insurance and reinsurance contracts known as ART (alternative risk transfer). The purpose of ART is to provide more efficient ways of risk transfer by combining insurance and reinsurance techniques with capital market techniques, and by accessing new sources of risk capital.
Catastrophe Excess of Loss
Authors: Mata Ana J.
Published: September 2014

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.