bluuebunny/crossref_metadata_2025 huggingface dataset:
Teaching Online Comprehension Strategies Using Think‐Alouds
Authors: Kymes Angel
Published: February 2005

As new information and communication technologies permeate classrooms and libraries, educators have the responsibility to assist students in comprehending and understanding the information that is now available online. How can we instruct students to become skilled, strategic readers when they encounter online texts and hypertextual formats? By using a familiar technique, the verbal protocol or think‐aloud method, educators can help students monitor their own learning and develop metacognitive strategies during online reading. The think‐aloud as an instructional model for teaching online comprehension has roots in reading, cognition, and usability research. Through demonstration and explicit instruction in the use of mindful strategies, such as setting a purpose, questioning the text, and evaluating structures and forms, educators are able to give students skills for the comprehension of information in the online environment. These skills, when used in conjunction with Web‐searching strategies and site evaluation, should also provide students with the ability to plan for their use and dissemination of information, as they are both consumers and producers of ideas. Educators face the challenges of becoming more technologically literate and capable of integrating these new technologies with their existing literacy curricula.
Taken on Faith: Religion and Identity in Writing Classes
Authors: Williams Bronwyn T.
Published: February 2005

In exploring her uneasiness in dealing with issues of religion in her classroom, the author asks, “Should I guide students away from writing about issues that explicitly dealt with their faith? Should I impose an outright prohibition on such writing? Or should I find ways to engage with the issues and the perspectives that were so clearly important to these students?” This insightful and reflective essay highlights the connections between faith and identity and the role that literacy may play in expression of both.
Allowance for Cost of Claims in Bonus-Malus Systems
Authors: Pinquet Jean
Published: February 2005

The objective of this paper is to make allowance for cost of claims in experience rating. We design here a bonus-malus system for the pure premium of insurance contracts, from a rating based on their individual characteristics. Empirical results are presented, that are drawn from a French data base of automobile insurance contracts.
Relative Reinsurance Retention Levels
Authors: Dickson David C.M. , Waters Howard R.
Published: February 2005

The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti (1940). He considered retention levels as optimal if they minimised the variance of the insurer's profit from the portfolio subject to the constraint of a fixed level of expected profit. In this paper we consider a similar problem, changing the criterion for optimality to minimising the probability of ruin, either in discrete or continuous time. We investigate this problem through a series of case studies based on a real portfolio.
On Error Bounds for Approximations to Aggregate Claims Distributions
Authors: Dhaene Jan , Sundt Bjørn
Published: February 2005

In the present paper we discuss error bounds for approximations to aggregate claims distributions. We consider approximations to convolutions by approximating each of the distributions and taking the convolution of these approximations. For compound distributions we consider two classes of approximations. In the first class we approximate the counting distribution, but keep the severity distribution unchanged, whereas in the second class we approximate the severity distribution, but keep the counting distribution unchanged. We finally look at some examples.
Risk-Minimizing Hedging Strategies for Unit-Linked Life Insurance Contracts
Authors: Møller Thomas
Published: February 2005

A unit-linked life insurance contract is a contract where the insurance benefits depend on the price of some specific traded stocks. We consider a model describing the uncertainty of the financial market and a portfolio of insured individuals simultaneously. Due to incompleteness the insurance claims cannot be hedged completely by trading stocks and bonds only, leaving some risk to the insurer. The theory of risk-minimization is briefly reviewed and applied after a change of measure. Risk-minimizing trading strategies and the associated intrinsic risk processes are determined for different types of unit-linked contracts. By extending the model to the situation where certain reinsurance contracts on the insured lives are traded, the direct insurer can eliminate the risk completely. The corresponding self-financing strategies are determined.
Modeling and Comparing Dependencies in Multivariate Risk Portfolios
Authors: Bäuerle Nicole , Müller Alfred
Published: February 2005

In this paper we investigate multivariate risk portfolios, where the risks are dependent. By providing some natural models for risk portfolios with the same marginal distributions we are able to compare two portfolios with different dependence structure with respect to their stop-loss premiums. In particular, some comparison results for portfolios with two-point distributions are obtained. The analysis is based on the concept of the so-called supermodular ordering. We also give some numerical results which indicate that dependencies in risk portfolios can have a severe impact on the stop-loss premium. In fact, we show that the effect of dependencies can grow beyond any given bound.
On the Analysis of the Truncated Generalized Poisson Distribution Using a Bayesian Method
Authors: Scollnik David P.M.
Published: February 2005

The generalized Poisson distribution with parameters θ and λ was introduced by Consul and Jain (1973) and has recently found several instances of application in the actuarial literature. The most frequently used version of the distribution assumes that θ > 0 and 0 ≤ λ < 1, in which case the mean and variance are θ/(1 − λ) and θ/(1 − λ)3, respectively. These simple moment expressions, along with nearly all of the other theoretical results available for this distribution, fail when λ < 0 or λ > 1 (e.g., Johnson, Kotz, and Kemp, 1992, page 397). In these cases, even the definition of the probability mass function usually given in the literature is not properly normalized so that its values do not sum to unity. For this reason, it is common to truncate the support of the distribution and explicitly normalize the probability mass function. In this paper we discuss the estimation of the parameters of this truncated generalized Poisson distribution using a Bayesian method.
A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover
Authors: Berglund Raoul M.
Published: February 2005

In the present paper the author gives net premium formulae for a generalized largest claims reinsurance cover. If the claim sizes are mutually independent and identically 3-parametric Pareto distributed and the number of claims has a Poisson, binomial or negative binomial distribution, formulae are given from which numerical values can easily be obtained. The results are based on identities for compounded order statistics.
Robust Bayesian Credibility Using Semiparametric Models
Authors: Young Virginia R.
Published: February 2005

In performing Bayesian analysis of insurance losses, one usually chooses a parametric conditional loss distribution for each risk and a parametric prior distribution to describe how the conditional distributions vary across the risks. Young (1997) applies techniques from nonparametric density estimation to estimate the prior and uses the estimated model to calculate the predictive mean of future claims given past claims. A shortcoming of this method is that, in estimating the prior, one assumes the average claim amount equals the conditional claim. In this paper, we consider a class of priors obtained by perturbing the one determined nonparametrically, as in Young (1997). We thereby reflect the uncertainty in the prior that arises from the randomness in the claim data. We, then, calculate intervals for the corresponding predictive means. We illustrate our method with data from Dannenburg et al. (1996) and compare the intervals of the predictive means with nonparametric confidence intervals.
Largest Claims Reinsurance Premiums under Possible Claims Dependence
Authors: Kremer Erhard
Published: February 2005

Largest claims reinsurance covers are reconsidered. Allowing the original claims sizes to be not necessarily independent, a new, upper premium bound is derived and explored.
Prediction of Outstanding Liabilities II. Model Variations and Extensions
Authors: Norberg Ragnar
Published: February 2005

This is a follow-up of a previous paper by the author, where claims reserving in non-life insurance is treated in the framework of a marked Poisson claims process. A key result on decomposition of the process is generalized, and a number of related results are added. Their usefulness is demonstrated by examples and, in particular, the connection to the analogous discrete time model is clarified. The problem of predicting the outstanding part of reported but not settled claims is revisited and, by way of example, solved in a model where the partial payments are governed by a Dirichlet process. The process of reported claims is examined, and its dual relationship to the process of occurred claims is pointed out.
Markov Chain Monte Carlo Estimation of Regime Switching Vector Autoregressions
Authors: Harris Glen R.
Published: February 2005

Financial time series data are typically found to possess leptokurtic frequency distributions, time varying volatilities, outliers and correlation structures inconsistent with linear generating processes, nonlinear dependence, and dependencies between series that are not stable over time. Regime Switching Vector Autoregressions are of interest because they are capable of explaining the observed features of the data, can capture a variety of interactions between series, appear intuitively reasonable, are vector processes, and are now tractable.

This paper considers a vector autoregression subject to periodic structural changes. The parameters of a vector autoregression are modelled as the outcome of an unobserved discrete Markov process with unknown transition probabilities. The unobserved regimes, one for each time point, together with the regime transition probabilities, are determined in addition to the vector autoregression parameters within each regime.

A Bayesian Markov Chain Monte Carlo estimation procedure is developed which efficiently generates the posterior joint density of the parameters and the regimes. The complete likelihood surface is generated at the same time, enabling estimation of posterior model probabilities for use in non-nested model selection. The procedure can readily be extended to produce joint prediction densities for the variables, incorporating both parameter and model uncertainty.

Results using simulated and real data are provided. A clear separation of the variance between a stable and an unstable regime was observed. Ignoring regime shifts is very likely to produce misleading volatility estimates and is unlikely to be robust to outliers. A comparison with commonly used models suggests that Regime Switching Vector Autoregressions provide a particularly good description of the observed data.
Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting
Authors: Grübel Rudolf , Hermesmeier Renate
Published: February 2005

Numerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.
The Exponential Premium Calculation Principle Revisited
Authors: Denuit Michel
Published: February 2005

In this paper, it is shown how to approximate theoretical premium calculation principles in order to make them useful in practice. The method relies on stochastic extrema in moment spaces and is illustrated with the aid of the exponential principle.
On the Distribution of the Surplus Prior and at Ruin
Authors: Schmidli Hanspeter
Published: February 2005

Consider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the case of subexponential distributions and some intermediate cases are discussed.
Selection of Credibility Regression Models
Authors: Bühlmann Peter , Bühlmann Hans
Published: February 2005

We derive some decision rules to select best predictive regression models in a credibility context, that is, in a “random effects’ linear regression model with replicates. In contrast to usual model selection techniques on a collective level, our proposal allows to detect individual structures, even if they disappear in the collective.

We give exact, non-asymptotic results for the expected squared error loss for a predictor based on credibility estimation in different models. This involves correct accounting of random model parameters and the study of expected loss for shrinkage estimation. We support the theoretical properties of the new model selectors by a small simulation experiment.
Recursive Evaluation of Some Bivariate Compound Distributions
Authors: Vernic Raluca
Published: February 2005

In this paper we consider compound distributions where the counting distribution is a bivariate distribution with the probability function (Pn1,n2)n1,n2≥0 that satisfies a recursion in the form

We present an algorithm for recursive evaluation of the corresponding compound distributions and some examples of distributions in this class.
Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System
Authors: Shengwang Meng , Wei Yuan , Whitmore G.A.
Published: February 2005

Individual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).
The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor
Authors: Mack Thomas
Published: February 2005

In Mack (1993), a formula for the standard error or chain ladder reserve estimates has been derived. In the present communication, a very intuitive and easily programmable recursive way of calculating the formula is given. Moreover, this recursive way shows how a tail factor can be implemented in the calculation of the standard error.
Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time
Authors: Cairns Andrew
Published: February 2005

This paper discusses the modelling and control of pension funds.

A continuous-time stochastic pension fund model is proposed in which there arenrisky assets plus the risk-free asset as well as randomness in the level of benefit outgo. We consider Markov control strategies which optimise over the contribution rate and over the range of possible asset-allocation strategies.

For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. Furthermore, the asset allocation strategy always lies on the capital market line familiar from modern portfolio theory.

A general quadratic loss function is proposed which provides an explicit solution for the optimal contribution and asset-allocation strategies. It is noted that these solutions are not dependent on the level of uncertainty in the level of benefit outgo, suggesting that small schemes should operate in the same way as large ones. The optimal asset-allocation strategy, however, is found to be counterintuitive leading to some discussion of the form of the loss function. Power and exponential loss functions are then investigated and related problems discussed.

The stationary distribution of the process is considered and optimal strategies compared with dynamic control strategies.

Finally there is some discussion of the effects of constraints on contribution and asset-allocation strategies.
A Multivariate Generalization of the Generalized Poisson Distribution
Authors: Vernic Raluca
Published: February 2005

This paper proposes a multivariate generalization of the generalized Poisson distribution. Its definition and main properties are given. The parameters are estimated by the method of moments.
On Multivariate Vernic Recursions
Authors: Sundt Bjørn
Published: February 2005

In the present paper we extend a recursive algorithm developed by Vernic (1999) for compound distributions with bivariate counting distribution and univariate severity distributions to more general multivariate counting distributions.
Long-Term Returns in Stochastic Interest Rate Models: Applications
Authors: Deelstra Griselda
Published: February 2005

We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral . For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.
Multivariate Compound Poisson Distributions and Infinite Divisibility
Authors: Sundt Bjørn
Published: February 2005

In this note we give a multivariate extension of the proof of Ospina & Gerber (1987) of the result of Feller (1968) that a univariate distribution on the non-negative integers is infinitely divisible if and only if it can be expressed as a compound Poisson distribution.
Credible Claims Reserves: the Benktander Method
Authors: Mack Thomas
Published: February 2005

A claims reserving method is reviewed which was introduced by Gunnar Benktander in 1976. It is a very intuitive credibility mixture of Bornhuetter/Ferguson and Chain Ladder. In this paper, the mean squared errors of all 3 methods are calculated and compared on the basis of a very simple stochastic model. The Benktander method is found to have almost always a smaller mean squared error than the other two methods and to be almost as precise as an exact Bayesian procedure.
Optimal Insurance Coverage under Bonus-Malus Contracts
Authors: Holtan Jon
Published: February 2005

The paper analyses the questions: Should – or should not – an individual buy insurance? And if so, what insurance coverage should he or she prefer? Unlike classical studies of optimal insurance coverage, this paper analyses these questions from a bonus-malus point of view, that is, for insurance contracts with individual bonus-malus (experience rating or no-claim) adjustments. The paper outlines a set of new statements for bonus-malus contracts and compares them with corresponding classical statements for standard insurance contracts. The theoretical framework is an expected utility model, and both optimal coverage for a fixed premium function and Pareto optimal coverage are analyzed. The paper is an extension of another paper by the author, see Holtan (2001), where the necessary insight to – and concepts of – bonus-malus contracts are outlined.
Introduction to Dynamic Financial Analysis
Authors: Kaufmann Roger , Gadmer Andreas , Klett Ralf
Published: February 2005

In the last few years we have witnessed growing interest in Dynamic Financial Analysis (DFA) in the nonlife insurance industry. DFA combines many economic and mathematical concepts and methods. It is almost impossible to identify and describe a unique DFA methodology. There are some DFA software products for nonlife companies available in the market, each of them relying on its own approach to DFA. Our goal is to give an introduction into this field by presenting a model framework comprising those components many DFA models have in common. By explicit reference to mathematical language we introduce an up-and-running model that can easily be implemented and adjusted to individual needs. An application of this model is presented as well.
Heavy-Tailed Distributions and Rating
Authors: Beirlant J. , Matthys G. , Dierckx G.
Published: February 2005

In this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.
Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes
Authors: Usábel M.
Published: February 2005

A method of inverting the Laplace transform based on the integration between zeros technique and a simple acceleration algorithm is presented. This approach was designed to approximate ultimate ruin probabilities for Γ-convolutions claim sizes, but it can be also used with other distributions. The stable algorithm obtained yields interval approximations (lower and upper bounds) to any desired degree of accuracy even for very large values of u (1,000,000), initial reserves, without increasing the number of computations. This last fact can be considered an interesting property compared with other recursive methods previously used in actuarial literature or other methods of inverting Laplace transforms.
The Mixed Bivariate Hofmann Distribution
Authors: Walhin J.F. , Paris J.
Published: February 2005

In this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case.

We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature.

This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution.
Maxima of Sums of Heavy-Tailed Random Variables
Authors: Ng K.W. , Tang Q.H. , Yang H.
Published: February 2005

In this paper, we investigate asymptotic properties of the tail probabilities of the maxima of partial sums of independent random variables. For some large classes of heavy-tailed distributions, we show that the tail probabilities of the maxima of the partial sums asymptotically equal to the sum of the tail probabilities of the individual random variables. Then we partially extend the result to the case of random sums. Applications to some commonly used risk processes are proposed. All heavy-tailed distributions involved in this paper are supposed on the whole real line.
On the Ruin Probability Under a Class of Risk Processes
Authors: Rongming Wang , Haifeng Liu
Published: February 2005

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the finite time ruin probability is well given when the claim amount distribution is a mixed exponential. As its consequence, a well-known result about ultimate ruin probability in the classical risk model is obtained.
Analytical Bounds for two Value-at-Risk Functionals
Authors: Hürlimann Werner
Published: February 2005

Based on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.
On Characterization of Distortion Premium Principle
Authors: Wu Xianyi , Wang Jinglong
Published: February 2005

In this paper, based on the additive measure integral representation of a non-additive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.
On the Density and Moments of the Time of Ruin with Exponential Claims
Authors: Drekic Steve , Willmot Gordon E.
Published: February 2005

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.
A Gaussian Exponential Approximation to Some Compound Poisson Distributions
Authors: Hürlimann Werner
Published: February 2005

A three parameter Gaussian exponential approximation to some compound Poisson distributions is considered. It is constructed by specifying the reciprocal of the mean excess function as a linear affine function below some threshold and a positive constant above this threshold. As an analytical approximation to compound Poisson distributions, it is only feasible either for a limited range of the Poisson parameter or for higher coefficients of variation. A semiparametric determination of the unknown threshold parameter is proposed. The analysis of a real-life example from pension fund mathematics displays an improved quality of fit of the new model when compared with other simple good alternative approximations based on the zero gamma, translated gamma and zero translated gamma.
Equilibrium Pricing Transforms: New Results Using Buhlmann’s 1980 Economic Model
Authors: Wang Shaun S.
Published: February 2005

In this paper we revisit an economic model of Buhlmann (ASTIN Bulletin, 1980) and derive equilibrium pricing transforms. We obtain the Esscher Transform and the Wang Transform under different sets of assumptions on the aggregate economic environment. We show that the Esscher Transform and the Wang Transform exhibit very different behaviors when used in pricing insurance risks.
Asymptotic Value-at-Risk Estimates for Sums of Dependent Random Variables
Authors: Wüthrich Mario V.
Published: February 2005

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.
New Econ for Life Actuaries
Authors: Aase Knut K. , Persson Svein-Arne
Published: February 2005

In an editorial in ASTIN BULLETIN, Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teaching since the beginning of the 90's at the Norwegian School of Economics and Business Administration (NHH). In this short note we point out that there may be some practical problems when these principles are to be implemented.
Optimal Dynamic XL Reinsurance
Authors: Hipp Christian , Vogt Michael
Published: February 2005

We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.
The Markov Chain Market
Authors: Norberg Ragnar
Published: February 2005

We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.
Pension Funding and the Actuarial Assumption Concerning Investment Returns
Authors: Owadally M. Iqbal
Published: February 2005

An assumption concerning the long-term rate of return on assets is made by actuaries when they value defined-benefit pension plans. There is a distinction between this assumption and the discount rate used to value pension liabilities, as the value placed on liabilities does not depend on asset allocation in the pension fund. The more conservative the investment return assumption is, the larger planned initial contributions are, and the faster benefits are funded. A conservative investment return assumption, however, also leads to long-term surpluses in the plan, as is shown for two practical actuarial funding methods. Long-term deficits result from an optimistic assumption. Neither outcome is desirable as, in the long term, pension plan assets should be accumulated to meet the pension liabilities valued at a suitable discount rate. A third method is devised that avoids such persistent surpluses and deficits regardless of conservatism or optimism in the assumed investment return.
Interest-Rate Changes and the Value of a Non-life Insurance Company
Authors: Albrecht Thomas ,   Allianz AG
Published: February 2005

How does a change in the risk-free interest-rate affect the value of a non-life insurance company or portfolio? Risk managers typically argue that there should be little impact as long as assets and liabilities are properly matched. However, the risk-management perspective focuses on existing assets and liabilities, while neglecting the value of future business potential. This paper argues that interest-rate changes can have a significant impact on the appraisal value of a non-life insurance company, even if assets and liabilities are matched. This impact can be positive as well as negative, depending on the underlying parameters. Relevant parameters include reserving intensity, combined ratio, business growth-rate, asset allocation, risk-capital relative to premium income and the correlation between interest-rate and technical insurance results.
On Merton’s Problem for Life Insurers
Authors: Steffensen Mogens
Published: February 2005

This paper deals with optimal investment and redistribution of the free reserves connected to life and pension insurance contracts in form of dividends and bonus. Formulated appropriately this problem can be viewed as a modification of Merton’s problem of optimal consumption and investment with a very particular form of consumption and utility hereof. Both are linked to a finite state Markov chain. We distinguish between utility optimization of dividends, where a semi-explicit result is obtained, and utility optimization of bonus payments. The latter connects to the financial notion of durable goods and allows for an explicit solution only in very special cases.
An Extension of the Gerber-Bühlmann-Jewell Conditions for Optimal Risk Sharing
Authors: Kaluszka Marek
Published: February 2005

We provide necessary and sufficient conditions for optimality of mutual contracts for risk sharing under constraints on premiums or utility functions of participants of the agreement. These conditions are an extension of those of the Borch, Gerber and Bühlmann-Jewell ones. Some applications to optimal insurance contracts, optimal dividend sharing and optimal reinsurance are given.
Some Optimal Dividends Problems
Authors: Dickson David C.M. , Waters Howard R.
Published: February 2005

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.
On the Maximisation of the Adjustment Coefficient under Proportional Reinsurance
Authors: Hald Morten , Schmidli Hanspeter
Published: February 2005

In this note we consider how to maximise the adjustment coefficient in the case of proportional reinsurance. This complements some work of Waters (1983), where it was shown that there is a unique retention level maximising the adjustment coefficient. The advantage of our method is that only one implicit equation has to be solved.
Testing for Concordance Ordering
Authors: Cebrián Ana C. , Denuit Michel , Scaillet Olivier
Published: February 2005

We propose inference tools to analyse the concordance (or correlation) order of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a probability that two variables are simultaneously small or large at least as great as it would be were they left unspecified. Tests for its generalisation in higher dimensions, namely joint lower and upper orthant dominance, are also analysed. The parametric and semiparametric settings are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. A distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US insurance claim data.
Application of Frailty-Based Mortality Models Using Generalized Linear Models
Authors: Butt Zoltan , Haberman Steven
Published: February 2005

Two families of frailty models – Makeham/Gompertz-gamma and Gompertz-inverse Gaussian – have been considered to graduate insurance-based mortality data. The aims of this exercise are twofold. The first aim is to make use of generalized linear models and to evaluate these against traditional techniques. The second aim is to measure the scale of individual heterogeneity in insurance-based populations. The results indicate that (subject to issues of identifiability) there is evidence of frailty in these populations.
The Sample Size Needed for the Calculation of a GLM Tariff
Authors: Schmitter Hans
Published: February 2005

A simple upper bound for the variance of the frequency estimates in a multivariate tariff using class criteria is deduced. This upper bound is based exclusively on univariate statistics and can, therefore, be calculated before a GLM analysis is carried out. It can be used to estimate the number of claims that will be needed for a tariff calculation depending on the number of tariff criteria and the number of levels of each criterion.

The article is a revised version of a paper presented at the XXXIst ASTIN Colloquium in Porto Cervo.
Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times
Authors: Avram F. , Usábel M.
Published: February 2005

This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion.

From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times.

In the case when the claims distribution is of phase-type as well, we obtain also an alternative formula for the single Laplace transform in time (or “exponentially killed probability’’), in terms of the roots with positive real part of the Lundberg’s equations, which complements Asmussen’s representation (1992) in terms of the roots with negative real part.
Risk Theory with the Generalized Inverse Gaussian Lévy Process
Authors: Morales Manuel
Published: February 2005

Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such model is either a compound Poisson process itself or a strictly increasing Lévy process. Their construction is based on a non-negative non-increasing function Q that governs the jumps of the process. This function, it turns out, is the tail of the Lévy measure of the process. We discuss an illustration of their model using a generalized Inverse Gaussian (GIG) Lévy process. This increasing Lévy process has the gamma and the inverse Gaussian process as particular cases. Although mathematically more complex, the GIG Lévy process keeps some of the nice properties of the simpler gamma process.
A Functional Approach to Approximations for the Individual Risk Model
Authors: Pitts Susan M.
Published: February 2005

A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.
The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles
Authors: Braun Christian
Published: February 2005

It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.
The Treatment of Assets in Pension Funding
Authors: Owadally M. Iqbal , Haberman Steven
Published: February 2005

A recent survey of actuarial practitioners in North America shows that smoothed-market actuarial asset values are commonly used in funding valuations of defined benefit pension plans. Four methods of calculating such values are reported in the actuarial literature but only qualitative descriptions of the methods are given. This paper provides mathematical descriptions of the “average of market”, “weighted average”, “deferred recognition” and “write-up” actuarial values. They are shown to be based on either arithmetic or exponential smoothing. Provided the same form of smoothing is used, the four methods are equivalent.
Awareness-Raising in the TEFL Phonology Classroom
Authors: Zhang Lawrence
Published: February 2005

This paper reports on two phases of a study of a group of advanced TEFL (teachers-of-English-as-a-foreign-language) students. To raise their awareness of the importance of discourse intonation while they were receiving teacher training, this study focuses on examining their sociocultural and psychological inclinations in the choice of phonological models. The first phase is an exploration of their attitudes toward, a native-speaker variety (British English) and a nonnative (Chinese EFL-speaker) variety of English pronunciation and intonation. The second reports on a didactic intervention study of the impact of activities that engaged the students in the awareness-raising of the importance of suprasegmental features, especially discourse intonation, on self-perceptions of their efficacy and confidence in communication. The results showed a systematic pattern of participant endorsement for a native-speaker model and a clear improvement in theIr perceptions of the importance of suprasegmental features of standard English because of teacher-student co-construction of meaning through interactive awareness-raising activities. The findings are discussed with reference to the students' sociocultural and psychological needs in TEFL training, particularly with reference to recent academic discourse on the issue of “linguistic imperialism” (Canagarajah, 1999; Phillipson, 1992, 1996) and ElL in pedagogy (Jenkins, 1998, 2002) and their wider implications in typical EFL contexts.
The struggle for meaning and power in HIV/AIDS education
Authors: Cervero Ronald M.
Published: February 2005

Strategies of response for HIV/AIDS education should account for structural relations of power, be culturally relevant to its audiences, and have the community as the focus of the intervention.
HIV‐positive adults' meaning making over time
Authors: Baumgartner Lisa M.
Published: February 2005

This chapter examines how HIV‐positive adults made sense of their diagnosis. Individuals experienced a perspective transformation or change in worldview, which was found to hold over time. Changes in meaning schemes or individual beliefs and assumptions occurred over time.
HIV/AIDS community‐based research
Authors: Trussler Terry , Marchand Rick
Published: February 2005

Community‐based research has evolved in the field of HIV/AIDS health promotion as a distinct expression of participatory action research in adult education. The authors of this chapter reflect on more than a decade of local knowledge construction to organize and improve the practice of HIV/AIDS health promotion in a variety of contexts.
Asserting a positive role: HIV‐positive people in prevention
Authors: Allan Brent , Leonard William
Published: February 2005

The best HIV prevention programs—those that effect change on a multiplicity of levels by changing knowledge, attitudes, and behaviors and that are sustained over time—are also those that place HIV‐positive people at the center of program design, implementation, and evaluation.
Risk assessment of migration from packaging materials into foodstuffs
Authors: Vitrac O. , Hayert M.
Published: February 2005

This work proposes a generic quantitative methodology to assess the risk of the migration of chemicals from packaging materials into foodstuffs. The distribution of the concentration in food is derived from a stochastic resolution of dimensionless transport equations accounting for physical properties of the considered food product(s) (solid/liquid, volume), of the packaging material(s) (polymer type, thickness), and of possible migrants (initial concentration, diffusion and partition coefficients at the temperature of storage). Each parameter is decomposed as a product of a scale factor and a dimensionless random contribution with known distributions (normal, log‐normal, Weibull, gamma, and beta). Nonlinear dependencies between all parameters (up to 12) are reliably handled based on projection techniques and convolution products. The proposed methodology is illustrated on three arbitrary classes of packed food products combined with two migration scenarios and three typical boundary conditions (solid food, liquid food, no‐external transport resistance). Finally, data analysis abacuses are provided to appraise the migration risk for more general cases. © 2005 American Institute of Chemical Engineers AIChE J, 2005
Intracranial arterial dolichoectasia and small‐vessel disease in stroke patients
Authors: Pico Fernando , Labreuche Julien , Touboul Pierre‐Jean , Leys Didier , Amarenco Pierre ,   for the GENIC Investigators
Published: February 2005

Two studies found that stroke patients with intracranial arterial dolichoectasia (IADE) had lacunar infarction more often than the control subjects. The relation between IADE and other manifestations of small‐vessel disease (multilacunar state, leukoaraiosis, and état criblé) was not investigated. The magnetic resonance images of 510 patients with brain infarction in the Etude du Profil Genetique de l'Infarctus Cerebral (GENIC) study were evaluated for the diagnosis of multilacunar infarction (>1 lacunar infarct), leukoaraiosis (assessed in periventricular and subcortical regions according to Scheltens and colleagues' scale, with severe leukoaraiosis defined as a score > 8), état criblé (using a semiquantitative score ranging from 0–8, with severe EC > 4), and IADE (using the consensus method). By comparison with stroke patients without IADE (n = 447), IADE(+) stroke patients (n = 63) had significantly more frequent multilacunar state (51 vs 33%), severe leukoaraiosis (34 vs 19%), and severe état criblé (32 vs 12%). After adjustment for potential confounding factors, the odds ratios (95% confidence interval) for the presence of IADE were 2.05 (1.08–3.87) for multilacunar state, 2.40 (1.11–5.20) for severe leukoaraiosis, and 3.60 (1.43–9.08) for severe état criblé. The factors significantly associated with état criblé were older age and a familial history of stroke. IADE in stroke patients was independently associated with parenchymal manifestations of small‐vessel disease. These conditions may have in common underlying pathophysiological processes. Ann Neurol 2005