(2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.

Comparison Methods for Stochastic Models and Risks

The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website.

Actuarial Theory for Dependent Risks: Measures, Orders and Models

Mixed Poisson distributions have been used in a wide range of scientific fields for modelling non-homogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures. A selective presentation of some of the most prominent members of the family of Poisson mixtures is made.

Mixed Poisson Distributions

Summary Mixed Poisson distributions have been used in a wide range of scientific fields for modeling non homogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures. A selective presentation of some of the most prominent members of the family of Poisson mixtures is made.

Application of the essential work of fracture (EWF) concept for polymers, related blends and composites: A review

There are a wide range of variables for actuaries to consider when calculating a motorist’s insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists’ rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information.

Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems

For the constructmn of bonus-malus systems, we propose to show how to apply, thanks to sunple mathematms, a parametric method encompassing those encountered m the hterature. We also compare this parametric method with a non-paramemc one that has not yet been used m the actuarial hterature and that however permits a simple formulatmn of the stationary and transmon probabflmes m a portfoho whenever we have the mtent~on to construct a bonus-malus system with fimte number of classes

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Using Mixed Poisson Processes in Connection with Bonus-Malus Systems

The precision of the measurement of the essential work of fracture requires an accurate determination of the critical ligament length below which the ligament is in a mixed mode stress state and the failure mechanisms considerably change. A statistical procedure is proposed which allows to determine easily and accurately this critical ligament length. After rejection of the specimens having too small ligament lengths, we is obtained by extrapolation of the remaining data for zero ligament length. The number of data points from which we is calculated is also shown to strongly influence the precision of the measurement. The procedure is applied to the measurement of the toughness of sheets of Al and Zn alloys and of a low density polyethylene.

Statistical procedure for improving the precision of the measurement of the essential work of fracture of thin sheets

In this paper, we propose an analytic analogue to the simulation procedure described in Taylor (1997). We apply the formulas to a Belgian data set and discuss the interaction between a priori and a posteriori ratemakings.

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Setting a bonus-malus scale in the presence of other rating factors: Taylor's work revisited

In this paper we investigate how to estimate ultimate values of large losses. The method is based on the development of individual losses and therefore allows to compute the netting impact of excess of loss reinsurance. In particular the index clause is properly accounted for. A numerical example based on real-life data is provided. © 2012 Taylor and Francis Group, LLC.

Jean-François Walhin

Papers

Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems

Using Mixed Poisson Processes in Connection with Bonus-Malus Systems

Statistical procedure for improving the precision of the measurement of the essential work of fracture of thin sheets

Setting a bonus-malus scale in the presence of other rating factors: Taylor's work revisited

Stochastic projection for large individual losses