Actuarial Theory for Dependent Risks
Measures, Orders and Models
Published on 1. May 2006
458 pages
978-0-470-01644-2 (ISBN)
Description
The increasing complexity of insurance and reinsurance products hasseen a growing interest amongst actuaries in the modelling ofdependent risks. For efficient risk management, actuaries need tobe able to answer fundamental questions such as: Is the correlationstructure dangerous? And, if yes, to what extent? Therefore toolsto quantify, compare, and model the strength of dependence betweendifferent risks are vital. Combining coverage of stochastic orderand risk measure theories with the basics of risk management andstochastic dependence, this book provides an essential guide tomanaging modern financial risk.
* Describes how to model risks in incomplete markets, emphasisinginsurance risks.
* Explains how to measure and compare the danger of risks, modeltheir interactions, and measure the strength of theirassociation.
* Examines the type of dependence induced by GLM-based credibilitymodels, the bounds on functions of dependent risks, andprobabilistic 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 conceptsby all levels of readers.
* Solutions to tasks as well as further examples and exercises canbe found on a supporting website.
An invaluable reference for both academics and practitioners alike,Actuarial Theory for Dependent Risks will appeal to all those eagerto master the up-to-date modelling tools for dependent risks. Theinclusion of exercises and practical examples makes the booksuitable for advanced courses on risk management in incompletemarkets. Traders looking for practical advice on insurance marketswill also find much of interest.
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07/2006
Wiley
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Michel Denuit | Jan Dhaene | Marc Goovaerts
Actuarial Theory for Dependent Risks
Measures, Orders and Models
Book
07/2005
Wiley
€137.50
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Persons
Michel Denuit - Michel Denuit is Professor ofStatistics and Actuarial Science at the Université catholiquede Louvain, Belgium. His major fields of research are risk theoryand stochastic inequalities. He (co-)authored numerous articlesappeared in applied and theoretical journals and served as memberof the editorial board for several journals (including Insurance:Mathematics and Economics). He is a section editor on Wiley'sEncyclopedia of Actuarial Science.
Jan Dhaene, Faculty of Economics and Applied EconomicsKULeuven, Belgium.
Marc Goovaerts, Professor of Actuarial Science (Non-lifeInsurance) at University of Amsterdam (The Netherlands) andCatholique University of Leuven (Belgium)
Rob Kaas, Professor of Actuarial Science (ActuarialStatistics), U. Amsterdam, The Netherlands.
Content
Foreword.
Preface.
PART I: THE CONCEPT OF RISKS.
1. Modelling Risks.
1.1 Introduction.
1.2 The Probabilitsic Description of Risks.
1.3 Indepenance for Events and Conditional Probabilities.
1.4 Random Variables and Vectors.
1.5 Distribution Functions.
1.6 Mathematical Expectation.
1.7 Transforms.
1.8 Conditional Ditsributions.
1.9 Comonotonicity.
1.10 Mutual Exclusivity.
1.11 Exercises.
2. Measuring Risk.
2.1 Introduction.
2.2 Risk Measures.
2.3 Value-at-Risk.
2.4 Tail Value-at-Risk.
2.5 Risk MEasures Based on Expected Utility Theory.
2.6 Risk Measures Based on Distorted Expectation Theory.
2.7 Exercises.
2.8 Appendix: Convexity and Concavity.
3. Comparing Risks.
3.1 Introduction.
3.2 Stochastic Order Relations.
3.3 Stochastic Dominance.
3.4 Convex and Stop-Loss Orders.
3.5 Exercises.
PART II: DEPENDANCE BETWEEN RISKS.
4. Modelling Dependence.
4.1 Introduction.
4.2 Sklar's Representation Theorem.
4.3 Families of Bivariate Copulas.
4.4 Properties of Copulas.
4.5 The Archimedean Family of Cpoulas.
4.6 Simulation from Given Marginals and Copula.
4.7 Multivariate Copulas.
4.8 Loss-Alae Modelling with Archimedean Copulas: A CaseStudy.
4.9 Exercises.
5. Measuring Depenence.
5.1 Introduction.
5.2 Concordance Measures.
5.3 Dependence Structures.
5.4 Exercises.
6. Comparing Depe6.1 Introduction.
6.2 Comparing in the Bivariate Case Using the CorrelationOrder.
6.3 Comparing Dependence in the Multivariate Case Using theSupermodular Order.
6.4 Positive Orthant Depenedence Order.
6.5 Exercises.
PART III: APPLICATIONS TO INSURANCE MATHEMATICS.
7. Depenedence in Credibility Models Based on Generalized LinearModels.
7.1 Introduction.
7.2 Poisson Static Credibility for Claim Frequencies.
7.3 More Results for the Static Credibility Model.
7.4 More Results for the Dynamic Credibility Models.
7.5 On the Depenedence Induced By Bonus-Malus Scales.
7.6 Credibility Theory and Time Series for Non-Normal Data.
7.7 Exercises.
8. Stochastic Bounds on Functions of Dependent Risks.
8.1 Introduction.
8.2 Comparing Risks with Fixed Depoenedence Structure.
8.3 Stop-Loss Bounds on Functions of Dependent Risks.
8.4 Stochastic Bounds on Functions of Dependent Risks.
8.5 Some Financial Applications.
8.6 Exercises.
9. Integral Orderings and Probability Metrics.
9.1 Introduction.
9.2 Integral Stochastic Oredrings.
9.3 Integral Probability Metrics.
9.4 Total-Variation Distance.
9.5 Kolmogorov Distance.
9.6 Wasserstein Distance.
9.7 Stop-Loss Distance.
9.8 Integrated Stop-Loss Distance.
9.9 Distance Between the Individual and Collective Models inRisk Theory.
9.10 Compound Poisson Approximation for a Portfolio of DependentRisks.
9.11 Exercises.
References.
Index.
