bluuebunny/crossref_metadata_2025 huggingface dataset:
Using the Picture Book Thank You, Mr. Falker to Understand Struggling Readers
Authors: Zambo Debby
Published: February 2005

Using picture books in teacher education courses allows instructors to set theory in context, create a visual representation of it, and make theory come alive. The benefit of picture books does not stop at the college door, because when students graduate and have classrooms of their own they can use the stories and pictures to remember and apply theories in their classrooms. Teachers who understand theory develop new ways of thinking and possess better problem‐solving skills, and are better prepared to assist struggling adolescent readers who need cognitive, social, and emotional support. In this article, Thank You, Mr. Falker by Patricia Polacco is used to demonstrate the power of picture books when professors use them in their classrooms and when teachers, in turn, use them in theirs. Ideas for sparking discussion in the college classroom are provided, along with nonthreatening activities that teachers of adolescents can use. Activities are designed to enliven domains of knowledge like history, current affairs, and writing and to enhance social and emotional skills. The ideas presented can build resilience in struggling readers and empathy and moral reasoning in their peers. Ten additional picture books are presented as extensions and enrichment of ideas.
On the Duality of Assumptions Underpinning the Construction of Life Tables
Authors: Renshaw A. E. , Haberman S. , Hatzopoulos P.
Published: February 2005

We investigate the implications of a dual approach to the graduation of the force of mortality based on the modelling of the exposures as gamma random variables, as opposed to the modelling of the numbers of deaths as Poisson random variables.
A Frequency Distribution Method for Valuing Average Options
Authors: Neave Edwin H.
Published: February 2005

This paper finds payoff frequency distributions for valuing European and American fixed strike average options on a discrete time, recombining multiplicative binomial asset price process. In comparison to other discrete valuation methods the distributions, obtained analytically from a generating function, greatly reduce the computational requirements needed for accurate valuation. Less data are needed to value geometric than arithmetic averages, but the magnitude of calculations is similar for both instruments. Calculations of orderT3are needed to value European instruments, of orderT4to value their American counterparts. A frequency distribution of a quantity calledpath sumsis used to value geometric average options, and a joint distribution of path sums and realized prices is used to value arithmetic average options. The frequency distributions give an exact value for geometric average, an approximate value for arithmetic average instruments. The method obtains additional information from the generating function to estimate approximation errors relative to the exact binomial solution. If the errors are significant they can be reduced using still further detail from the generating function. Error reduction can be performed selectively to minimize additional calculation.
A New Distribution of Poisson-Type for the Number of Claims
Authors: Denuit Michel
Published: February 2005

This paper is concerned with two methods to estimate the parameters of the Poisson-Goncharov distribution introduced recently by Lefevre and Picard (1996). These methods are applied to fit, inter alia, the six observed claims distributions, from automobile insurance third party liability portfolios, studied by Gossiaux and Lemaire (1981) and analysed afterwards by several authors.
Calculating Ruin Probabilities via Product Integration
Authors: Ramsay Colin M. , Usabel Miguel A.
Published: February 2005

When claims in the compound Poisson risk model are from a heavy-tailed distribution (such as the Pareto or the lognormal), traditional techniques used to compute the probability of ultimate ruin converge slowly to desired probabilities. Thus, faster and more accurate methods are needed. Product integration can be used in such situations to yield fast and accurate estimates of ruin probabilities because it uses quadrature weights that are suited to the underlying distribution. Tables of ruin probabilities for the Pareto and lognormal distributions are provided.
Simulation of Ruin Probabilities for Subexponential Claims
Authors: Asmussen S. , Binswanger K.
Published: February 2005

We consider the classical risk model with subexponential claim size distribution. Three methods are presented to simulate the probability of ultimate ruin and we investigate their asymptotic efficiency. One, based upon a conditional Monte Carlo idea involving the order statistics, is shown to be asymptotically efficient in a certain sense. We use the simulation methods to study the accuracy of the standard Embrechts-Veraverbeke [16] approximation for the ruin probability and also suggest a new one based upon ideas of Hogan [21].
Setting a Bonus-Malus Scale in the Presence of other Rating Factors
Authors: Taylor Greg
Published: February 2005

The operation of a bonus-malus system, superimposed on a premium system involving a number of other rating variables, is considered. To the extent that good risks are rewarded in their base premiums, through the other rating variables, the size of the bonus they require for equity is reduced. This issue is discussed quantitatively, and a numerical example given.
An Integrated Dynamic Financial Analysis and Decision Support System for a Property Catastrophe Reinsurer
Authors: Lowe Stephen P. , Stanard James N.
Published: February 2005

This paper describes the dynamic financial analysis model currently being used by a property catastrophe reinsurer to manage its business. The model is-an integral part of the day-to-day operations at the Company, and is used as a decision making tool in the underwriting, investment, and capital management processes. The paper begins by describing the framework that the Company uses for risk management. This includes a classification of the risks facing the Company, which is used to define and prioritize their implementation in the model. Also included is a description of the conceptual approach the Company takes to evaluate the tradeoff between risk and return. The paper then goes on to describe the structure and operation of the dynamic financial analysis model and provides examples of its use at the Company, along with illustrative examples of the various types of output it produces.
APS Reinsurance
Authors: Koller Bruno , Dettwyler Nicole
Published: February 2005

This paper presents a new reinsurance product, called ‘Adaptive Pivot Smoothing’ (APS). It is designed to reduce the variance of the risk reinsured without affecting the mean. Investment theories have provided the idea for the product.
Withdrawal Benefits under a Dependent Double Decrement Model
Authors: Carriere Jacques F.
Published: February 2005

This article presents an explicit formula for the value of a withdrawal benefit when the times of death and withdrawal are dependent. The derivation is based on an actuarial equivalence principle. As a special case, we show that in the fully continuous case, the withdrawal benefit is the reserve when the decrements are independent. We also present a definition of antiselection and prove that the withdrawal benefit will be smaller under antiselection.
The Cox Regression Model for Claims Data m Non-Life Insurance
Authors: Keiding Niels , Andersen Christian , Fledelius Peter
Published: February 2005

The Cox regression model is a standard tool in survival analysis for studying the dependence of a hazard rate on covariates (parametrically) and time (nonparametrically). This paper is a case study intended to indicate possible applications to non-life insurance, particularly occurrence of claims and rating.

We studied individuals from one Danish county holding policies in auto, property and household insurance simultaneously at some point during the four year period 1988-1991 in one company. The hazard of occurrence of claims of each type was studied as function of calendar time, time since the last claim of each type, age of policy holder, urbanization and detailed type of insurance. Particular emphasis was given to the technical advantages and disadvantages (particularly the complicated censoring patterns) of considering the nonparametrically underlying time as either calendar time or time since last claim. In the former case the theory is settled, but the results are somewhat complicated. The latter choice leads to several issues still under active methodological development. We develop a goodness-of-fit criterion which shows the lack of fit of some models, for which the practical conclusions might otherwise have been useful.
Comparing Risk Adjusted Premiums from the Reinsurance Point of View
Authors: e Silva João Manuel Andrade , Centeno Maria de Lourdes
Published: February 2005

In this paper we compare, from the point of view of reinsurance, the several risk adjusted premium calculation principles considered in Wang (1996b). We conclude that, with the exception of the proportional hazard (PH) premium calculation principle, all the others behave in a way similar to the expected value principle. We prove that the stop loss reinsurance premium when calculated using the PH premium principle gives a higher premium than any of the other transforms, provided that the priority is big enough. We observe a similar behaviour with respect to excess of loss reinsurance in all the examples given.

We also study the behaviour of the adjustment coefficient, both from the insurer's and the reinsurer's point of view as functions of the priority, when the PH principle is used as opposed to the expected value principle.
A Credibility Approach to Mortality Risk
Authors: Hardy M.R. , Panjer H.H.
Published: February 2005

Bühlmann-Straub credibility is used to find an estimate of the mortality loss ratio for a company, relative to a standard table, for use in the statutory valuation of life insurance business. A method for calculating the margin for adverse deviation to be added to the mortality rate (in accordance with the general principle of Canadian statutory valuation) is derived. Applying credibility further to the variance of the mortality loss ratio gives a methodology for calculating the amount of the surplus (i.e. capital) required to cover annual fluctuations in mortality experience. The necessary structural parameters are calculated from industry statistics; the methodology is illustrated using Canadian life insurance data.
Using Mixed Poisson Processes in Connection with Bonus-Malus Systems
Authors: J.F. Walhin  , Paris J.
Published: February 2005

For the construction of bonus-malus systems, we propose to show how to apply, thanks to simple mathematics, a parametric method encompassing those encountered in the literature. We also compare this parametric method with a non-parametric one that has not yet been used in the actuarial literature and that however permits a simple formulation of the stationary and transition probabilities in a portfolio whenever we have the intention to construct a bonus-malus system with finite number of classes.
Stochastic Pension Funding: Proportional Control and Bilinear Processes
Authors: Bédard Diane
Published: February 2005

In this paper, we find explicit expressions for the moments of the fund level and the value of the total contribution when arithmetic or geometric rates of return are modeled by a moving average process of order q and when a proportional control is applied to the contributions. Our approach is based on the bilinear Markovian representation.
Multi-Period Aggregate Loss Distributions for a Life Portfolio
Authors: C.M. Dickson David , Waters Howard R.
Published: February 2005

Algorithms for the calculation of the distribution of the aggregate claims from a life insurance portfolio have been derived by Kornya (1983), Hipp (1986) and De Pril (1986 and 1989). All these authors considered the distribution of the aggregate claims over a single period. In this paper we derive algorithms for the calculation of the joint distribution of the aggregate claims from a life portfolio over several periods.
Discussion on D.C.M. Dickson & H.R. Waters Multi-Period Aggregate Loss Distributions for a Life Portfolio
Authors: Sundt Bjørn
Published: February 2005

In the present discussion we point out the relation of some results in Dickson & Waters (1999) to similar results in Sundt (1998a, b).

We shall need some notation. For a positive integer m let m be the set of all m × 1 vectors with positive integer-valued elements and m+ = m ~ {0}. A vector will be denoted by a bold-face letter and each of its elements by the corresponding italic with a subscript denoting the number of the elements; the subscript · denotes the sum of the elements. Let m0 be the class of probability functions on m with a positive probability at 0 and m+ the class of probability functions on m+. For j = 1,…, m we introduce the m × 1 vector ej where the jth element is one and all the other elements zero. We make the convention that summation over an empty range is equal to zero.

Let g ∈ m0 be the compound probability function with counting distribution with probability function v ∈ 10 and severity distribution with probability function h ∈ m+; we shall denote this compound probability function by v V h. Sundt (1998a) showed that

where φv denotes the De Pril transform of v, given by

Motivated by (2) Sundt (1998a) defined the De Pril transform φg of g by

This defines the De Pril transform for all probability functions in m0. Insertion of (2) in (3) gives

and by solving φg(X) we obtain

Sundt (1998a) studies the De Pril transform defined in this way and found in particular that it is additive for convolutions.
Estimating Per Capita Expenses in Multiple State Models of Permanent Health Insurance
Authors: Kovářová Marie
Published: February 2005

The aim of this work is to present a method to compute the expected amount of annual claims in the health insurance. (A more detailed analysis of the method can be found in Kovářová (1998).) We will be especially concerned with the permanent health insurance and compare our numerical results with those computed and published for the permanent health insurance in C.M.I.R. (1991). At the same time we will give a general methodology applicable not only to the permanent health insurance but for other types of health insurance as well.

The methods used today can be divided into three groups: the method of the decrement tables, the Manchester Unity method and the multiple state model. We would like to describe a simple method to compute from the data of the multiple state model the bases for the Manchester United and for the decrement tables methods.
Recursive Formulae for Some Bivariate Counting Distributions Obtained by the Trivariate Reduction Method
Authors: Walhin J.F. , Paris J.
Published: February 2005

In this paper we study some bivariate counting distributions that are obtained by the trivariate reduction method. We work with Poisson compound distributions and we use their good properties in order to derive recursive algorithms for the bivariate distribution and bivariate aggregate claims distribution. A data set is also fitted.
Portfolio Optimization
Authors: Schnieper René
Published: February 2005

Based on the profit and loss account of an insurance company we derive a probabilistic model for the financial result of the company, thereby both assets and liabilities are marked to market. We thus focus on the economic value of the company.

We first analyse the underwriting risk of the company. The maximization of the risk return ratio of the company is derived as optimality criterion. It is shown how the risk return ratio of heterogeneous portfolios or of catastrophe exposed portfolios can be dramatically improved through reinsurance. The improvement of the risk return ratio through portfolio diversification is also analysed.

In section 3 of the paper we analyse the loss reserve risk of the company. It is shown that this risk consists of a loss reserve development risk and of a yield curve risk which stems from the discounting of the loss reserves. This latter risk can be fully hedged through asset liability matching.

In section 4 we derive our general model. The portfolio of the company consists of a portfolio of insurance risks and of a portfolio of financial risks. Our model allows for a simultaneous optimization of both portfolios of risks. A theorem is derived which gives the optimal retention policy of the company together with its optimal asset allocation.

Some of the material presented in this paper is taken from Schnieper, 1997. It has been repeated here in order to make this article self contained.
Pricing Risk Transfer Transactions
Authors: Lane Morton N.
Published: February 2005

Should the pricing of reinsurance catastrophes be related to the price of the default risk embedded in corporate bonds?

If not, why not?

A risk is a risk is a risk, in whatever market it appears. Shouldn't the risk-prices in these different markets be comparable? More basically perhaps, how should reinsurance prices and bond prices be set? How does the market currently set them? These questions are central to the inquiry contained in this paper.

Avoiding unnecessary suspense, our answers are: Yes, cat prices should be related to credit prices because both risks contain a characteristic trade-off between the frequency of and severity of adverse events. We leave the question of how prices should be set to others and focus on the empirical question of how they have been set by the markets. In the process, we develop a fairly robust pricing mechanism and explore its potential uses in many different contexts.

The 1999 Insurance-Linked Securities (ILS) market (a.k.a., Cat Bond market) provides the empirical springboard to the discussion. The ILS market is only 4 years old. As such, it represents a new and unique intersection of reinsurance and financial markets. It provides a wonderful laboratory for exploring risk-pricing.

The ILS market, still in its experimental phase, appears to require more generous (cheap) pricing of insurance risk than does the bond market of default risk. So much so that academics have begun to weigh in on the question of why. Previously, insurance pricing discussions had been confined to practicing insurance professionals, particularly actuaries. For finance professionals, insurance pricing, much less reinsurance pricing, seldom made the index of their financial texts – though even that is beginning to change.
Computation of Compound Distributions II: Discretization Errors and Richardson Extrapolation
Authors: Grübel Rudolf , Hermesmeier Renate
Published: February 2005

The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.
Pricing Excess of Loss Reinsurance with Reinstatements
Authors: Mata Ana J.
Published: February 2005

In this paper we discuss the concept of excess of loss reinsurance with reinstatements. The main objective is to provide a methodology to calculate the distribution of total aggregate losses for two or more consecutive layers when there is a limited number of reinstatements. We also compare different premium principles and their properties to price these treaties for any number of free or paid reinstatements.
The True Claim Amount and Frequency Distributions within a Bonus-Malus System
Authors: Walhin Jean François , Paris José
Published: February 2005

We apply Lemaire's algorithm and a non-parametric mixed Poisson fit to a motor insurance portfolio in order to find the true claim frequency and claim amount distributions. The algorithm we develop accounts for the fact that observed distributions are distorted by bonus hunger, when a bonus-malus system is used by the insurer.
Credibility Weighted Hazard Estimation
Authors: Nielsen Jens Perch , Sandqvist Bjørn Lunding
Published: February 2005

Credibility weighting is helpful in many insurance applications where sparse data crave information from other sources of data. In this paper we aim at estimating a hazard curve using the nonparametric kernel method, where a credibility weighting principle is used locally, so that areas of sparse data for one subgroup can be alleviated by available information from other subgroups. The credibility estimator is found through a Hilbert space projection formulation of Buhlmann-Straub's credibility approach.
Insurance Premium Calculations with Anticipated Utility Theory
Authors: Luan Cuncun
Published: February 2005

This paper examines an insurance or risk premium calculation method called the mean-value-distortion pricing principle in the general framework of anticipated utility theory. Then the relationship between comonotonicity and independence is explored. Two types of risk aversion and optimal reinsurance contracts are also discussed in the context of the pricing principle.
Experience Rating Schemes for Fleets of Vehicles
Authors: Desjardins Denise , Dionne Georges , Pinquet Jean
Published: February 2005

This paper proposes bonus-malus systems for fleets of vehicles, by using the individual characteristics of both the vehicles and the carriers. Bonus-malus coefficients are computed from the history of claims or from the history of safety offences of the carriers and the drivers. The empirical results are derived from a data set obtained from the Société de l'Assurance Automobile du Québec, the public insurer for bodily injuries and the regulator of road safety.
The Natural Sets of Wang's Premium Principle
Authors: Wu Xian-Yi
Published: February 2005

Recently, Wang's premium principle (Wang, 1995, 1996) has been discussed by many authors. Considerable attention has been given to the conditions under which Wang's premium principle can be reduced to the standard deviation premium principle. In this paper, we have got two results on this problem. One is that the natural set is a location-scale family if Wang's premium principle can be reduced to the SD premium principle for all surjective distortions. The other is that the natural set is a location-scale family for all power distortions.
Geographic Premium Rating by Whittaker Spatial Smoothing
Authors: Taylor Greg
Published: February 2005

Whittaker graduation is applied to the spatial smoothing of insurance data. Such data (e.g. claim frequency) form a surface over the 2-dimensional geographic domain to which they relate. Observations on this surface are subject to sampling error. They need to be smoothed spatially if a reliable estimate of the underlying surface is to be obtained.

A measure of smoothness of a surface has been defined. This has been incorporated in 2-dimensional Whittaker graduation to effect the necessary smoothing. The details of this are worked out in Section 4. The procedure is illustrated by numerical example in Section 5. The Bayesian interpretation of this form of spatial smoothing is discussed, and used to assist in the selection of the Whittaker relativity constant.
A Nelson-Aalen Estimate of the Incidence Rates of Early-Onset Alzheimer's Disease Associated with the Presenilin-1 Gene
Authors: Gui Eng Hock , Macdonald Angus
Published: February 2005

We analyse, in a probabilistic setting, Newcombe's (1981) life table method of estimating rates of onset of high-penetrance single-gene disorders, and extend this to a counting process model for individual life histories, including movement between risk groups arising from genetic testing and onset in relatives. A key result is that estimates of rates of onset at any age x must be conditioned only on information available when subjects were age x, even though their later life histories might be available to the investigator. This determines the data that must be included in pedigrees. We derive a Nelson-Aalen-type estimate of a function of the rate of onset, and show that when all that is known is that the persons in the study inherited a mutation with probability 1/2, the function estimated is bounded. In practice, the treatment of censored observations or the methods of ascertainment might cause the estimate to exceed this bound, which results in infinite estimates of the rate of onset but might be a useful diagnostic check on the presence of these features. We summarise the literature on mutations in the Presenilin-1 (PSEN-1) gene, associated with early-onset Alzheimer's disease (EOAD), and from published pedigrees we estimate rates of onset of EOAD.
On Error Bounds for Approximations to Multivariate Distributions II
Authors: Sundt Bjørn , Vernic Raluca
Published: February 2005

In the present paper, we study error bounds for approximations to multivariate distributions. In particular, we discuss some general versions of compound multivariate distributions and look at distributions of dependent random variables constructed by linear transforms of independent random variables or vectors. Special attention is paid to the case when the support of the original distribution is restricted. We also look at some applications with multivariate Bernoulli distributions.
A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum
Authors: Kaas R. , Dhaene J. , Vyncke D. , Goovaerts M.J. , Denuit M.
Published: February 2005

In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X1X2, …, Xn) with given marginals has a comonotonic joint distribution, the sum X1 + X2 + … + Xn is the largest possible in convex order. In this note we give a lucid proof of this fact, based on a geometric interpretation of the support of the comonotonic distribution.
On the Safety Loading for Chain Ladder Estimates: a Monte Carlo Simulation Study
Authors: Schiegl M.
Published: February 2005

A method for analysing the risk of taking a too low reserve level by the use of Chain Ladder method is developed. We give an answer to the question of how much safety loading in terms of the Chain Ladder standard error has to be added to the Chain Ladder reserve in order to reach a specified security level in loss reserving. This is an important question in the framework of integrated risk management of an insurance company. Furthermore we investigate the relative bias of Chain Ladder estimators. We use Monte Carlo simulation technique as well as the collective model of risk theory in each cell of run-off table. We analyse deviation between Chain Ladder reserves and Monte Carlo simulated reserves statistically. Our results document dependency on claim number and claim size distribution types and parameters.
Dynamic Programming Approach to Pension Funding: the Case of Incomplete State Information
Authors: Haberman S. , Sung Joo-Ho
Published: February 2005

Haberman and Sung (1994) have presented a dynamic model for a defined benefit occupational pension scheme which considered two types of risk: the “contribution rate” and the “solvency” risk. The current paper, extends this work by deriving optimal funding control procedures for determining the contribution rate for the case of a stochastic model with incomplete state information, making use of the separation principle. The stochastic inputs modelled are the investment returns and the benefit outgo.
Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling
Authors: Smyth Gordon K. , Jørgensen Bent
Published: February 2005

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit,μsay. They observed that the dependence of the likelihood function onμis as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.
An Extension of Panjer's Recursion
Authors: Hess Klaus Th. , Liewald Anett , Schmidt Klaus D.
Published: February 2005

Sundt and Jewell have shown that a nondegenerate claim number distribution Q = {qn}nϵN0 satisfies the recursion

for all n≥0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n ≥ 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n ≥ k with arbitrary k. Our results are of interest in catastrophe excess-of-loss reinsurance.
The Distribution of the time to Ruin in the Classical Risk Model
Authors: Dickson David C.M. , Waters Howard R.
Published: February 2005

We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.
Dependence in Dynamic Claim Frequency Credibility Models
Authors: Purcaru Oana , Denuit Michel
Published: February 2005

In nonlife insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account (in the spirit of the Bühlmann-Straub model). This paper aims to study the kind of dependence induced by the introduction of correlated latent variables in the annual numbers of claims reported by policyholders. The effect of reporting claims on the a posteriori distribution of the random effects will be made precise. This will be done by establishing some stochastic monotonicity property of the a posteriori distribution with respect to the claims history.
Comment on the Discussion Article by Aase and Persson
Authors: Bühlmann Hans
Published: February 2005

I applaud the article as it is exactly the type of reaction to my editorial in Astin Bulletin 32(2) that I hoped to provoke. Of course Aase and Persson's contribution is much more academic in style than mine which is more journalistic.

To my understanding there are three important messages on which every reader of their article should reflect.
Guaranteed Annuity Options
Authors: Boyle Phelim , Hardy Mary
Published: February 2005

Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.

The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.
A Discrete Time Benchmark Approach for Insurance and Finance
Authors: Bühlmann Hans , Platen Eckhard
Published: February 2005

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure transformation is needed for the fair pricing of insurance policies and derivatives. The standard actuarial pricing rule is obtained as a particular case of fair pricing when the contingent claim is independent from the growth optimal portfolio.

1991 Mathematics Subject Classification: primary 90A12 secondary 60G30, 62P20

JEL Classification: G10, G13
A Unified Approach to Generate Risk Measures
Authors: Goovaerts Marc J. , Kaas Rob , Dhaene Jan , Tang Qihe
Published: February 2005

The paper derives many existing risk measures and premium principles by minimizing a Markov bound for the tail probability. Our approach involves two exogenous functions v(S) and φ(S, π) and another exogenous parameter α ≤ 1. Minimizing a general Markov bound leads to the following unifying equation:

E [φ (S, π)] = αE [v (S)].

For any random variable, the risk measure π is the solution to the unifying equation. By varying the functions φ and v, the paper derives the mean value principle, the zero-utility premium principle, the Swiss premium principle, Tail VaR, Yaari's dual theory of risk, mixture of Esscher principles and more. The paper also discusses combining two risks with super-additive properties and sub-additive properties. In addition, we recall some of the important characterization theorems of these risk measures.
Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling
Authors: Lindskog Filip , McNeil Alexander J.
Published: February 2005

The idea of using common Poisson shock processes to model dependent event frequencies is well known in the reliability literature. In this paper we examine these models in the context of insurance loss modelling and credit risk modelling. To do this we set up a very general common shock framework for losses of a number of different types that allows for both dependence in loss frequencies across types and dependence in loss severities. Our aims are threefold: to demonstrate that the common shock model is a very natural way of approaching the modelling of dependent losses in an insurance or risk management context; to provide a summary of some analytical results concerning the nature of the dependence implied by the common shock specification; to examine the aggregate loss distribution that results from the model and its sensitivity to the specification of the model parameters.
Asymptotic Dependence of Reinsurance Aggregate Claim Amounts
Authors: Mata Ana J.
Published: February 2005

In this paper we study the asymptotic behaviour of the joint distribution of reinsurance aggregate claim amounts for large values of the retention level under various dependence assumptions. We prove that, under certain dependence assumptions, for large values of the retention level the ratio between the joint distribution of the aggregate losses and the product of the marginal distributions converges to a constant value that only depends on the frequency parameters.
Chain Ladder Bias
Authors: Taylor Greg
Published: February 2005

The chain ladder forecast of outstanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 5 shows that, under rather general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.
Claims Reserving Using Tweedie's Compound Poisson Model
Authors: Wüthrich Mario V.
Published: February 2005

We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.
Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data
Authors: Brazauskas Vytaras , Serfling Robert
Published: February 2005

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.
Prediction of Stock Returns: A New Way to Look at It
Authors: Nielsen Jens Perch , Sperlich Stefan
Published: February 2005

While the traditional R2 value is useful to evaluate the quality of a fit, it does not work when it comes to evaluating the predictive power of estimated financial models in finite samples. In this paper we introduce a validated value useful for prediction. Based on data from the Danish stock market, using this measure we find that the dividend-price ratio has predictive power. The best horizon for prediction seems to be four years. On a one year horizon, we find that while inflation and interest rate do not add to the predictive power of the dividend-price ratio then last years excess stock return does.
On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems
Authors: Sarabia José María , Gómez-Déniz Emilio , Vázquez-Polo Francisco J.
Published: February 2005

In this paper a new methodology using the conditional specification technique intoduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas.
Asset Allocation with Regime-Switching: Discrete-Time Case
Authors: Cheung Ka Chun , Yang Hailiang
Published: February 2005

In this paper, we study the optimal asset allocation problem under a discrete regime switching model. Under the short-selling and leveraging constraints, the existence and uniqueness of the optimal trading strategy are obtained. We also obtain some natural properties of the optimal strategy. In particular, we show that if there exists a stochastic dominance order relationship between the random returns at different regimes, then we can order the optimal proportions we should invest in such regimes.
An Accurate Asymptotic Approximation for Experience Rated Premiums
Authors: Gatto Riccardo
Published: February 2005

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.
Measuring Process Risk in Income Protection Insurance
Authors: Haberman Steven , Butt Zolan , Rickayzen Ben
Published: February 2005

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.
Testing Distributions of Stochastically Generated Yield Curves
Authors: Venter Gary G.
Published: February 2005

A method is introduced for testing the distribution of yield curves that are produced by asset scenario generators. The method is based on historical relationships in the conditional distributions of yield spreads given the short-term rate. As an illustration, this method is used to test a few selected models. To provide background, stochastic modeling for interest rates and fitting methods are briefly discussed.
Second Order Bayes Prediction of Functionals of Exponential Dispersion Distributions and an Application to the Prediction of the Tails
Authors: Landsman Zinoviy
Published: February 2005

Second order Bayes estimators, being the main tool in second order optimal statistical theory, provide a natural basis for a new approach to the problem of the prediction of functions of expectation functional for members of an exponential dispersion family. A general formula, providing such prediction up to the term of the order 1/n, is suggested and the application to the problem of the prediction of the tail of distributions is demonstrated. The results are illustrated with normal and gamma claim sizes. The numerical experiment demonstrates the high effectiveness of the approach even for small sample sizes.
Modeling and Generating Dependent Risk Processes for IRM and DFA
Authors: Pfeifer Dietmar , Nešlehová Johana
Published: February 2005

Modern Integrated Risk Management (IRM) and Dynamic Financial Analysis (DFA) rely in great part on an appropriate modeling of the stochastic behavior of the various risky assets and processes that influence the performance of the company under consideration. A major challenge here is a more substantial and realistic description and modeling of the various complex dependence structures between such risks showing up on all scales. In this presentation, we propose some approaches towards modeling and generating (simulating) dependent risk processes in the framework of collective risk theory, in particular w.r.t. dependent claim number processes of Poisson type (homogeneous and non-homogeneous), and compound Poisson processes.
An Application of Linear Programming to Bonus Malus System Design
Authors: Heras Antonio , Gil José A. , García-Pineda Pilar , Vilar José L.
Published: February 2005

The purpose of this paper is to show how linear programming methodology can help us to design Bonus-Malus premium scales with some interesting theoretical and practical attributes. Examples of these properties are the financial equilibrium of the system, the monotonicity and proper variability of the premium scale, and the improvement of some efficiency measures such as the RSAL and the elasticity of the system. We will conclude that the use of the linear programming methodology makes possible a high degree of interaction between the designer and the mathematical model.
Strategic Competence in an ELT Syllabus
Authors: Rabab'ah Ghaleb Ahmed
Published: February 2005

Communication strategies (CSs) are important in helping learners to communicate successfully when they are faced with a production problem due to their lack of linguistic knowledge. This paper aims to support the importance of developing second language learners’ strategic competence and making communication strategies part of an ELT syllabus. This paper first discusses the various definitions of strategic competence and communication strategies. Then it briefly presents various communication strategies used by second language learners to solve their communication problems. The major portion of this paper is devoted to strategy training and its advantages in language learning. Finally, the paper concludes with the importance of introducing tasks and activities on communication strategies in an EFL syllabus, and suggests ways of improving teaching methodology.
Bad blood: The Tuskegee syphilis study and legacy recruitment for experimental AIDS vaccines
Authors: Hagen Kimberly Sessions
Published: February 2005

For African Americans, medical research often connotes exploitation and cruelty, making recruiting African Americans to participate in HIV vaccine trials particularly daunting. But infusing adult education principles into such efforts is both increasing African American participation and helping heal the legacy of the Tuskegee experiment.
Grassroots response to HIV/AIDS in Nova Scotia
Authors: Plumb Donovan
Published: February 2005

This chapter describes how by adopting a cultural theory of learning, members of a community‐based research team deepened their understanding of the nature, pervasiveness, and contribution of everyday learning processes of people affected by HIV/AIDS in Nova Scotia, Canada.
Fast equivalent operational model of tropospheric alkane photochemistry
Authors: Wang S. W. , Balakrishnan S. , Georgopoulos P.
Published: February 2005

A mathematical “kinetic lumping” approach, the direct constrained approximate lumping (DCAL) method, for developing a condensed chemical mechanism of complex tropospheric alkane photochemistry was presented in previous work. In the present work, the high dimensional model representation (HDMR) method is applied to further accelerate the chemical kinetic calculations of the Alkane/DCAL mechanism from our previous work. An efficient HDMR is based on expressing a chemical species concentration at a given reaction time as an expansion of correlated functions consisting of the initial chemical species concentrations. An HDMR expansion calculates efficiently the output species concentrations at any given reaction time, employing very rapid and stable algebraic manipulations. The HDMR estimates are shown to be almost identical to those derived from solving the full tropospheric alkane photochemistry through conventional (for example, Gear‐type) chemistry solvers over wide ranges of initial conditions, while being more than 1,000 times faster. © 2005 American Institute of Chemical Engineers AIChE J, 2005