bluuebunny/crossref_metadata_2025_split huggingface dataset:
Genetic Algorithms in Reliability
Authors: Coit David W. , Taboada Heidi A. 
Published: September 2014

Abstract
Genetic algorithms (GAs) have been effectively used to solve many difficult engineering problems and are particularly effective for solving combinatorial optimization problems with large, complex search spaces. The redundancy allocation problem (RAP) is perhaps one of the most common problems in design for reliability and it is known to be NP hard. Redundancy is used as a strategy to meet high reliability specifications in many system design engineering projects. In this material, we present an overview of some of the most relevant research that has been done on the use of GAs in the reliability optimization of redundant systems.
Intensity Functions for Nonhomogeneous Poisson Processes
Authors: McCollin Christopher 
Published: September 2014

AbstractWhen analysing reliability data from a repairable system e.g. a car, a fridge, etc, reliability specialists are interested in the full life history of a system so that they may identify problems that have affected its life and apply solutions, if possible, to other new systems so that these new systems do not suffer from the same problems. The basis of reliability analysis is to understand how systems are failing by modeling their life history so that prediction of the likely future reliability of systems is possible. This is the basis of reliability growth (development) testing where systems under development are tested to find latent design and manufacturing defects so that they can be eliminated from the full‐scale production system.The simplest way of identifying structure in the system's life history is to plot the data. Three plots are commonly used: plotting failures on a time line; plotting the failure number against cumulative time, and plotting an estimate of the intensity, the rate of occurrence of failures (ROCOF) against cumulative time. These plots appear in Ascher and Feingold [31] and Crowderet al. [61] among others. These plots will help to identify structure such as an increase or decrease in the interfailure times of a system over time (more commonly known as reliability growth and reliability decay); evidence of cycles in the data—these may be short or long cycles; periods of high or low reliability (again related to usage); gaps in the time stream (due to change in the reporting mechanism, management, etc) and outliers (possible abnormal operating conditions).This review lists the intensity functions and their associated expected number of failures, which is the mean value parameter of the nonhomogeneous Poisson process (NHPP). The simplest and best known intensities, those based on mortality rates, those based on hazards of well‐known probability distributions, the software related intensities, and those based on differential equations and extensions are discussed under their appropriate classification headings.
Computational Issues in Network Reliability
Authors: Colbourn Charles J. , Shier Douglas R. 
Published: September 2014

AbstractSystems of interconnected components can often be usefully represented by networks. It is practically important to calculate the reliability of such network systems when the components are subject to (statistically independent) failures. We define several commonly occurring reliability models and summarize the computational complexity of calculating their associated reliability measures. Some general techniques for exact and approximate calculation of network reliability are surveyed.
D
e
P
ril Recursions and Approximations
Authors: Sundt Bjørn 
Published: September 2014

Abstract
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.
Heckman–Meyers Algorithm
Authors: Klugman Stuart A. 
Published: September 2014

Abstract
The collective risk model for aggregate losses states that total losses for a period comprise a random number of random payments where the payments have identical distributions and all variables are independent. Evaluating probabilities for this model can be difficult. The Heckman–Meyers Algorithm is one of several approaches to this problem. While computationally challenging, it is accurate and in many situations is extremely fast.
Claim Number Processes
Authors: Garrido José 
Published: September 2014

AbstractRisk theory models describe the uncertainty associated with the claims recorded by an insurance company for losses incurred by its policy holders. The claims frequency and the claims severity are two important components of these models. This article centers on models for the frequency of losses.Even if an insurance company were able to maintain the exact same portfolio of policies over time, the number of claims recorded would still vary from year to year. Such natural fluctuations are modeled through the claim number random variable.Over time, claim counts evolve according to a stochastic process: the claim number process. While other sections discuss specific claim number processes in greater detail, the general features are given here.
L
undberg Inequality for Ruin Probability
Authors: Yang Hailiang 
Published: September 2014

Abstract
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.
Actuarial Control Cycle
Authors: Bellis Clare 
Published: September 2014

Abstract
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.
Participating Business
Authors: David O'Brien Christopher 
Published: September 2014

AbstractIn 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.
Social Security
Authors: Eriksen Tor 
Published: September 2014

AbstractSocial security is a concept that can be interpreted in many different ways and should therefore be used with the utmost caution.Barr notes that in the United States, it refers to retirement pensions; in the United Kingdom, it refers to the entire system of cash benefits; and in mainland Europe (in accordance with the practice of the International Labor Organization), it refers to all cash benefits plus health care.Barr chooses to describe the security system by examining the purpose of the various cash benefits.Universal benefits awarded on the basis of a specified event, without regard to a person's income or contribution record. Examples include family allowance and free health care.Social assistance awarded on the basis of an income test and the occurrence of a specified event, without a contribution test.Consequently, social security can be seen as an accumulative concept for different systems that provide economical compensation in the case of illness, unemployment, old age, and so on.
Markov ChainMonteCarlo Methods
Authors: Roberts Gareth O. , Rosenthal Jeffrey S. 
Published: September 2014

AbstractOne of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called thetargetdensity) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scientific applications, for instance, Statistics, Computer Science, and Statistical Physics.Markov chain Monte Carlo offers an indirect solution based on the observation that it is much easier to construct an ergodic Markov chain with π as a stationary probability measure, than to simulate directly from π. This is because of the ingeniousMetropolis–Hastingsalgorithm, which takes an arbitrary Markov chain and adjusts it using a simple accept–reject mechanism to ensure the stationarity of π for the resulting process.
Simulation of Stochastic Processes
Authors: Asmussen Søren 
Published: September 2014

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.
Simulation of Risk Processes
Authors: Burnecki Krzysztof , Härdle Wolfgang , Weron Rafał 
Published: September 2014

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.
Esscher Transform
Authors: Yang Hailiang 
Published: September 2014

AbstractThis article surveys the main results and developments of Esscher transform. We first present the original idea of Esscher and its applications to the problem of approximating the tail probabilities. The Esscher transform applied to the premium calculation, the Esscher premium principle, is then discussed. Recently, the Esscher transform has been applied to finance to tackle the problem of option pricing. Following Gerber–Shiu's framework, we provide an overview on this interesting development.
Fuzzy Set Theory
Authors: A. Derrig Richard , M. Ostaszewski Krzysztof 
Published: September 2014

Abstract
Traditional actuarial methodologies have been built upon probabilistic models. They are often driven by stringent regulation of the insurance business. Deregulation and global competition of the last two decades have opened the door for new methodologies, among them, being fuzzy methods. The defining property of fuzzy sets is that their elements possibly have partial membership (between 0 and 1), with degree of membership of zero indicating not belonging to the set considered, and degree of membership of one indicating certainty of membership.
This article provides a quick overview of developing fuzzy sets methodologies in actuarial science, and the basic mathematics of fuzzy sets.
Random Variable, Overview
Authors: Asmussen Søren 
Published: September 2014

Abstract

In intuitive terms, a random variable (r.v.)
X
is a number, whose value is determined by random factors (chance). For example, the exchange rate Euro/USD next New Year or the number of car accidents in a certain month and county.

In the car accident example, the month may be in the past or in the future. In the first case,
X
is then completely known, say
X
= 738, and rather than as a r.v., one speaks of 738 as the
outcome
of the r.v.
X
. The precise interpretation of such issues in terms of the axioms for probability theory is discussed.

A r.v. is usually assumed to be real‐valued,
X
∈ Υ, like in the above examples. However, in principle also, other sets of values are possible. The most prominent example is multivariate r.v.s,
X
= (X
1
,…, X
d
) ∈ Υ
d
(e.g. the set of exchange rates in January,
d
= 31), which are discussed in detail in this article.

Random variables are one of the most fundamental concepts of probability theory and treated in any elementary or intermediate textbook.
Under‐ and Overdispersion
Authors: Xekalaki Evdokia 
Published: September 2014

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).
History of Actuarial Education
Authors: Forfar David O. 
Published: September 2014

Abstract
This article looks at the history of actuarial education where, from the start, there was a difference in approach between the Anglo‐Saxon world and Continental Europe. In the Anglo‐Saxon world, entry to the actuarial profession depended on passing the examinations set by the profession and it was not necessary to have gone to a university (although exemptions could be granted in certain countries from some of the earlier examinations if sufficient relevant academic training had been undertaken). In Continental Europe, entry to the profession depended, in the main, on having successfully completed the relevant courses at university (or technische hochschule) or having gained sufficient practical ‘on‐the‐job’ experience.
History of Insurance
Authors: Sibbett Trevor 
Published: September 2014

AbstractFrom 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.
Screening Methods
Authors: Malutov Michail , Wynn Henry P. , Zhigljavsky Anatoly 
Published: September 2014

AbstractScreening is a term applied to the general approach of detecting active or significant factors, elements, units, and so on when there are a large number of inactive factors. The meaning of ‘active’ depends on the context: effective treatments, presence of a disease, fault, etc. The methods are of considerable importance in medical and industrial applications. The theoretical aspects, particularly finding optimal or efficient experimental designs are closely related to search methods and special combinatorial constructions.
Parameter and Model Uncertainty
Authors: Cairns Andrew J.G. 
Published: September 2014

Abstract
Almost every actuarial problem involves one or more sources of risk. The task of an actuary is to assess the following risks:

To derive a distribution for the outcome at some fixed future time or at a series of future dates.

To make decisions or observations based on this risk assessment (e.g. to provide a risk measure, to set a premium rate, to calculate the reserve, to decide on an investment strategy).
Robustness in the Linear Regression M+N105odel
Authors: Hubert Mia , Rousseeuw Peter J. , Aelst Stefan 
Published: September 2014

AbstractWhen applying a statistical method in practice, it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that arerobust against the possibility that one or several unannounced outliers may occur anywhere in the data.
Graduation in Insurance
Authors: B. Miller Robert 
Published: September 2014

Abstract
In actuarial science, graduation refers to the adjustment of a set of estimated quantities to make the adjusted quantities conform to a pattern suitable for insurance purposes. We distinguish between two broad categories of approaches to actuarial graduation: those that involve fitting curves defined by functions and those that involve other methods. Curve‐fitting approaches use popular functional forms such as Gompertz, Weibull, Makeham, and splines. Non–curve‐fitting approaches in this article are grouped under the headings Weighted Moving Average Methods, Kernel Methods, Whittaker Methods, and Bayesian Methods.
Reliability Analysis
Authors: Natvig Bent 
Published: September 2014

AbstractIn reliability analysis, one is interested in studying the reliability of a technological system being small or large. As examples of small systems, we have washing machines and cars, whereas tankers, oil rigs, and nuclear power plants are examples of large systems. By the reliability of a system, we will mean the probability that it functions as intended. It might be tacitly assumed that we consider the system only for a specified period of time (for instance, one year) and under specified conditions (for instance, disregarding war actions and sabotage). Furthermore, one has to make clear what is meant by functioning. For oil rigs and nuclear power plants, it might be to avoid serious accidents such as a blowout or a core‐melt.Reliability analysis is a very helpful tool in risk assessment when determining the insurance premiums for risks, especially of rare events, associated with large systems consisting of both technological and human components. Furthermore, reliability analysis is relevant in risk management of any technological system, the aim now being to say something helpful on how to avoid accidents. This is an area of growing importance representing an enormous challenge for an insurance company.
Central Limit Theorem
Authors: Heyde C.C. 
Published: September 2014

AbstractTheCentral Limit Theorem(CLT) is generally regarded as a generic name applied to any theorem giving convergence in distribution, especially to the normal law, of normed sums of an increasing number of random variables. Results of this kind hold under far reaching circumstances, and they have, in particular, given the normal distribution a central place in probability theory and statistics.
Extreme Value Theory
Authors: Albin J.M.P. 
Published: September 2014

Abstract
In insurance one often has to deal with extremal measurements like large claims. Comparable to central limit theory for sums of random variables, extreme value theory provides asymptotic and approximating results for these largest data values. The case of independent claims can be dealt with using three traditional extremal types. These types also appear in the stationary case when the dependence is not too strong.
Stochastic Orderings: Theory
Authors: Denuit Michel , Müller Alfred 
Published: September 2014

Abstract
We describe the basic ideas of stochastic orders, which formally describe intuitive ideas like ‘being larger’, ‘being more variable’ or ‘being more dependent’ for risks or for portfolio of risks. We give the definitions of the most important stochastic orders like usual stochastic order, convex order, supermodular order and others, and we consider their most important properties and some applications.
Risk Management: An Interdisciplinary Framework
Authors: Tapiero Charles S. 
Published: September 2014

AbstractRisk management is shown to be based on both theory and practice. It is shown to be conceptual and technical, blending behavioral psychology, financial economics, and decision‐making under uncertainty into a coherent whole that justifies the selection of risky choices. Its applications are broadly distributed across many areas and fields of interest. The examples treated here have focused on both finance and insurance and on a few problems in industrial management.
Finance
Authors: Brockett Patrick 
Published: September 2014

Abstract
Finance and insurance are very similar in nature: they both (now) consider the value of a financial instrument or an insurance policy or a firm to be the discounted present value of the future cash flows they provide to their holder. Research in the fields of finance and insurance have been converging, with products and valuation techniques from one field applying to and being used in the other field. Risk pooling, risk sharing, and risk transfer are the essence of insurance and the topic of study in modern finance, with both fields interested in valuing contingent claims, either claims due to financial or liability obligations, market changes, foreign exchange rate, or due to interest rate changes or payments due, contingent upon the occurrence of a particular type of insured loss (e.g. fire insurance payments, life insurance payments, automobile insurance payments, etc.). Thus, finance and insurance are more and more linked, and products in each area are less and less distinct.
Mortality Laws
Authors: Forfar David O. 
Published: September 2014

AbstractSince the time of De Moivre in 1725, various mathematical formulae have been suggested to represent the pattern of mortality rates with age. Some of the formulae have applied at adult ages, some at very young ages, and some over the whole span of life. Certain formulae have been used in the graduation of mortality data. The article gives a survey of the mathematical laws used and examines how mortality might look in the foreseeable future if it goes on improving.