Actuarial Theory for Dependent Risks: Measures, Orders and Models
John Wiley & Sons, May 1, 2006 - Business & Economics - 458 pages
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.
An invaluable reference for both academics and practitioners alike, Actuarial Theory for Dependent Risks will appeal to all those eager to master the up-to-date modelling tools for dependent risks. The inclusion of exercises and practical examples makes the book suitable for advanced courses on risk management in incomplete markets. Traders looking for practical advice on insurance markets will also find much of interest.
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actuarial science Archimedean copulas associated assume bivariate comonotonic components conditional convex functions convex order copula credibility models decision-maker defined Definition denoted Denuit dependence structure df F X Dhaene distortion function equivalent Esscher Example Exercise expected utility theory F1 and F2 following result Fr´echet Fréchet function g Goovaerts holds identically distributed increasing increasingness independent and identically independent rvs integer-valued rvs joint df Laplace transform Let X1 log-concave loss monotone MTP2 multivariate normal distribution n-dimensional random vectors non-decreasing functions non-negative rv orthant parameter Poisson policyholder portfolio positive dependence probability metrics probability space Property Proposition PrX1 random couple random effects random variables random vector rank correlation coefficient risk measure Show stochastic dominance stochastic inequality stochastic orderings stop-loss order subadditive supermodular theorem TVaR univariate upper bound utility function VaRX X1 and X2 X1 X2 Xn