bluuebunny/crossref_metadata_2025_split huggingface dataset:
Pooling Equilibria
Authors: Boyer Marcel , Boyer M. Martin 
Published: September 2006

Abstract
We present in this paper, different contexts under which pooling equilibria emerge in insurance economics. A pooling equilibrium may emerge when it is not optimal (or not feasible or not allowed) to offer different contracts to different agents. As a result, agents with different risk types are ‘pooled’ together even though the low‐risk agents end up subsidizing the high‐risk agents. This subsidy, quite like an externality imposed by the high‐risk types on the low‐risk ones, may lead low‐risk insureds to try to identify themselves and insurers to search for different ways to bypass the pooling equilibrium by identifying and luring away good risk types, thereby destabilizing the pooling equilibrium.
Prediction
Authors: Schmidt Klaus D. 
Published: September 2006

Abstract
Rate making and loss reserving both require the prediction of future payments for claims. Whenever this is possible, the prediction of future payments is based on claims experience in the past and on assumptions describing the way in which future payments depend on those in the past.
Mathematically, it is convenient to describe all payments by random variables and to model dependencies between these random variables by an assumption on their joint probability distribution. The random variables describing the past are assumed to be observable and form the statistical basis for predicting the random variable describing the future.
The statistical basis can be used in various ways to construct predictors. Therefore, there is a need of criteria for the selection of the predictor to be used. The main criterion is the comparison of predictors by a suitable measure of quality; such a measure is not given by nature but has to be chosen by the actuary. In addition, a preselection can be made by the requirement of certain properties which the predictor to be selected should possess; one such property is unbiasedness which can be understood as a mathematical formulation of the actuarial principle of equivalence.
Present Values and Accumulations
Authors: Macdonald Angus S. 
Published: September 2006

Abstract

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.
Probability Theory
Authors: Hoffman‐Jørgensen J. 
Published: September 2006

Abstract
This article collects the basic concepts needed in all articles with a probabilistic undertone. After giving some historical development of probability concepts in insurance, the axiomatic concepts from probability theory are treated succinctly. Having dealt with the most common types of convergence, the most fundamental limit theorems are formulated with an indication of their interrelationship.
Profit Testing
Authors: Richards Stephen 
Published: September 2006

Abstract
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.
Queueing Theory
Authors: Sigman Karl 
Published: September 2006

Abstract

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
.
Random Walk
Authors: Doney R.A. 
Published: September 2006

Abstract

Random walks are the simplest of all stochastic processes; they include amenable examples of both Markov processes and martingales, and indeed the genesis of these two important classes of processes can be found in their study. Their origins lie in the first attempts to model gambling situations, and they still have many useful modeling applications. In actuarial mathematics, random walks occur widely in ruin theory. In discrete time, the surplus process (claims minus premiums) may be modeled as a random walk. In continuous time, the surplus observed at claim times is a random walk, for example, for the Sparre Andersen model. In both cases, the ruin probability is
P(M > u)
, where
u
is the initial reserve and
M
denotes the all‐time maximum of the random walk. The study of
M
also occurs in queueing theory, since it has the same distribution as the waiting time in a
GI/G/1
queue.
Regenerative Processes
Authors: Wolff Ronald W. 
Published: September 2006

Abstract
A regenerative process is a stochastic process with the property that after some (usually) random time, it starts over in the sense that, from the random time on, the process is stochastically equivalent to what it was at the beginning.
In many applied fields such as telecommunications, finance, and actuarial science, important probability models turn out to be regenerative. Properties of regenerative processes and the mathematical methods used in their analysis are fundamental in the analysis and understanding of these models.

For
classical
regenerative processes, cycles and cycle lengths are i.i.d. (independent and identically distributed). This assumption has been weakened over time. Now, processes satisfying the first paragraph above are regarded as regenerative, without any independent assumptions.

This article introduces the classical case in the section ‘Classical Regenerative Processes’, presents their time‐average properties in the section ‘Time‐average Properties, Classical Case’, and briefly treats more advanced topics in the section ‘Existence of Limits; Combining Processes’.
Resampling
Authors: Verrall Richard 
Published: September 2006

Abstract
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.
Reinsurance, Reserving
Authors: Radtke Michael 
Published: September 2006

Abstract
The article deals with actuarial reserving techniques used in reinsurance. The impact of reinsurance on the actuarial reserving approach is discussed with a focus on the actuarial methods. In reinsurance, very often, the standard methods, that is, Chain‐Ladder or Bornhuetter Ferguson have to be modified because of specific reinsurance requirements. We introduce some methodical adjustments and illustrate the practical circumstances under which they have been taken into account. The paper ends with some comments on practical applications of reserving methods in reinsurance.
Retrospective Premium
Authors: Meyers Glenn 
Published: September 2006

Abstract
Insurance is about the transfer of risk. If an entity, either a person or a business, wants to transfer all of its risk of loss to an insurer and the insurer is able to quantify the risk that the entity wishes to transfer, the price of the risk transfer is readily established by market forces and a deal is struck.
In many cases, the insurer is not confident that it can quantify the risk that the entity wishes to transfer. An entity sensing difficulty in getting a full transfer of risk may be willing to settle for a partial transfer of risk. The insurer would be more comfortable with a partial risk transfer because the entity has an incentive to keep its loss at a minimum.
This article describes a particular kind of risk‐sharing agreement called a retrospective rating plan. In these plans, the premium for an insurance contract is a function of the actual loss paid under the contract. The final premium is not known until after the contract has expired. This explains the name retrospective rating.
Risk Measures
Authors: Albrecht Peter 
Published: September 2006

AbstractThe 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.
Optimal Risk Sharing
Authors: Aase Knut K. 
Published: September 2006

Abstract
Optimal risk sharing is considered from the perspective of the risk sharing model introduced by Karl Borch in the late 50's. First we introduce, in a modern setting, the main concepts from this theory. These we apply on the risk sharing problem between an insurer and an insurance customer. We motivate the development through a simple example, illustrating some fine points of this theory. In order to explain deductibles, we introduce transaction costs that are paid out ex post. Moral hazard provides another example.
Severity of Ruin
Authors: Tsai Cary Chi‐Liang 
Published: September 2006

Abstract
In this article, continuous‐time risk models are introduced; the time of ruin, and the surplus immediately before and at ruin caused by a claim are defined. Then the probability of ruin, the (discounted) moment of the severity of ruin caused by a claim, the joint moment of the severity of ruin and the time of ruin caused by a claim, and the (discounted) defective joint/marginal distribution and probability functions of the surplus immediately before and at ruin are studied.
Simulation of Risk Processes
Authors: Burnecki Krzysztof , Härdle Wolfgang , Weron Rafał 
Published: September 2006

Abstract
The simulation of risk processes is a standard procedure for insurance companies. The generation of aggregate claims is vital for the calculation of the amount of loss that may occur. Simulation of risk processes also appears naturally in rating triggered step‐up bonds, where the interest rate is bound to random changes of the companies' ratings.
Simulation of Stochastic Processes
Authors: Asmussen Søren 
Published: September 2006

Abstract
In order to gain insight into the role played by the stochastic ingredients in insurance and finance, one is often forced to rely on simulation as no explicit analytic results are available. There exist a few general methods, but the generation on computer for most models requires non‐trivial and complicated operations that heavily depend on the specific structure of the underlying stochastic elements.
Stability
Authors: Rusaityte Deimante 
Published: September 2006

Abstract
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.
Subexponential Distributions
Authors: Klüppelberg Claudia 
Published: September 2006

AbstractSubexponential distributions are a special class of heavy‐tailed distributions. The name arises from one of their properties that their tails decrease slower than any exponential tail (3). This implies that large values can occur in a sample with nonnegligible probability, which makes the subexponential distributions natural candidates for modeling situations in which some extremely large values occur in a sample compared with the mean size of the data. Such a pattern is often seen in insurance data, for instance, in fire, wind–storm, or flood insurance (collectively known as catastrophe insurance). Subexponential claims can account for large fluctuations in the surplus process of a company, increasing the risk involved in such portfolios.
Surplus in Life and Pension Insurance
Authors: O'Brien Christopher David 
Published: September 2006

AbstractSurplus 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.
Survival Analysis
Authors: Veraverbeke Noël 
Published: September 2006

AbstractSurvival analysis deals with the statistical modeling and analysis of durations of time from some origin to some ‘failure’. Such lifetimes are usually subject to censoring and/or truncation. We survey the most important developments around the two main landmarks: the product‐limit estimator of Kaplan and Meier (1958) 58 and the proportional hazards regression model of Cox (1972) 23.
Reinsurance — Terms, Conditions, and Methods of Placing
Authors: Czapiewski Colin , Gates Paul 
Published: September 2006

Abstract
The placing of reinsurance business is changing, with the role of intermediaries and methods of placement being constantly assessed in light of the costs. Smaller lines with many reinsurers are being replaced by much larger lines with few reinsurers. New forms of reinsurance are being introduced to reflect the requirements of the reinsured more accurately. In view of the more legal examination of contracts, the accuracy of the terms, conditions, exclusions, and other aspects of policy wording are now more important than ever before.
Time of Ruin
Authors: Tsai Cary Chi‐Liang 
Published: September 2006

Abstract
In this article, both classical discrete‐ and continuous‐time risk models are introduced; then the time of ruin and the severity of ruin are defined. The probability of ruin and some quantities concerning the time of ruin, such as the expectation of the present value of the time of ruin, the (discounted) moment of the severity of ruin caused by a claim, the joint moment of the severity of ruin, and the time of ruin caused by a claim, and the moments of the time of ruin due to oscillation and claim, respectively, are studied.
Under‐ and Overdispersion
Authors: Xekalaki Evdokia 
Published: September 2006

AbstractVery often, in connection with applications, one is faced with data that exhibit a variability, which differs from that anticipated under the hypothesized model. This phenomenon is termedover dispersionif the observed variability exceeds the expected variability orunder dispersionif it is lower than expected.Such discrepancies between the empirical variance and the nominal variance can be interpreted to be induced by a failure of some of the basic assumptions of the model. These failures can be classified by how they arise, that is, by the mechanism leading to them. In traditional experimental contexts, for example, they are caused by deviations from the hypothesized structure of the population, such as lack of independence between individual item responses, contagion, clustering, and heterogeneity. In observational study contexts, they are the result of the method of ascertainment, which can lead to partial distortion of the observations. In both cases, the observed valuexdoes not represent an observation on the random variableX, but an observation on a random variableYwhose probability distribution (the observed probability distribution) is a distorted version of the probability distribution ofX(original distribution). This can have a variance greater than that anticipated under the original distribution (over dispersion) or, much less frequently in practice, lower than expected (under dispersion).
Valuation of Life Insurance Liabilities
Authors: O'Brien Christopher David 
Published: September 2006

AbstractPlacing a value on life insurance liabilities is not easy. The issues are not new: we can go back to 1864, when the British Prime Minister William Gladstone referred in Parliament to the accounts of the Prudential Assurance Company:‘As it stands, it presents a balance of £41,000 in favor of the society; but it has been examined by actuaries, and those gentlemen, proceeding upon principles which are no more open to question than a proposition of Euclid, say, that instead of a balance of £41,000 in favor of, there is one of £31,000 against the society’.In the twenty‐first century we still have debates on how to value the liabilities arising from life insurance policies, notably with the work of the International Accounting Standards Board in its effort to design an international financial reporting standard for insurance contracts, to be used in insurers' accounts.Key questions arewhat are the estimated future cash flows from a life policy? andwhat discount rate should be applied to the cash flows to derive a present value?Closely linked with these questions arehow should the uncertainty about the cash flows be reflected in the valuation? andhow can we ensure consistency of the valuation of the liabilities with the valuation of the insurers' assets?
Value‐at‐Risk
Authors: Dowd Kevin 
Published: September 2006

Abstract

The Value at Risk (VaR) on a portfolio is the maximum loss we might expect over a given period, at a given level of confidence. It is therefore defined over two parameters – the period concerned, usually known as the holding period, and the confidence level – whose values are arbitrarily chosen. The VaR is a relatively recent risk measure whose roots go back to Baumol, who suggested a risk measure equal to μ –
k
σ, where μ and σ are the mean and standard deviation of the distribution concerned, and
k
is a subjective parameter that reflects the user's attitude to risk. The term
value at risk
only came into widespread use much later. The notion itself lay dormant for nearly 30 years, and then shot to prominence in the early to mid 1990s as the centerpiece of the risk measurement models developed by leading securities firms. The most notable of these, Morgan's Risk‐Metrics model, was made public in October 1994, and gave rise to a widespread debate on the merits, and otherwise, of VaR. Since then, there have been major improvements in the methods used to estimate VaR, and VaR methodologies have been applied to other forms of financial risk besides the market risks for which it was first developed.
Workers' Compensation Insurance
Authors: Feldblum Sholom 
Published: September 2006

Abstract
Although some of the earliest workers' compensation systems were in Europe, many countries now have included recompense for worker injury into social welfare programs. Currently the largest system for which employers purchase private insurance for this matter is in the United States, and this will be the focus of this article. Each state has its own system, so some differences among these will be addressed. State workers' compensation systems developed in the early twentieth century to replace negligence liability for workplace accidents and illnesses. The development of workers' compensation rates by class and state sparked the emergence of the Casualty Actuarial Society (CAS) in 1914.
Magnetic Resonance Angiography
Authors: Yuan Chun 
Published: September 2006

AbstractAngiography generally refers to any imaging method that can visualize blood vessels. Magnetic resonance angiography (MRA) is a class of magnetic resonance (MR) imaging techniques that create blood vessel images. During the past decade, there has been a tremendous amount of development and refinement in MRA techniques, making MRA a powerful tool in the diagnosis of cardiovascular disease. In most of the cases, MRA techniques are applied noninvasively, without the use of ionizing radiation. The inherent advantages of MR imaging (noninvasive, flow sensitive, high soft tissue contrast, and flexible imaging approaches) make it ideally suited to the study of the vasculature in almost any part of the human body. MRA presents a wide spectrum of techniques for the study of flowing blood: different methods for high spatial resolution, high temporal resolution, velocity sensitization, flow quantification, and visualizing pulsatility. This article addresses the basic principles of MRA and describes its applications.