Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.]

• Pubblicazione: Hoboken, N.J., : Wiley, c2005
• Descrizione fisica: 1 online resource (460 p.)
• Disciplina: 368; 368/.001/51
• Soggetto topico: Risk (Insurance) - Mathematical models
• Soggetto genere / forma: Electronic books.
• Altri autori: DenuitM (Michel)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references p. ([422]-437) and index.
• Nota di contenuto: Actuarial Theory for Dependent Risks; Contents; Foreword; Preface; PART I THE CONCEPT OF RISK; 1 Modelling Risks; 1.1 Introduction; 1.2 The Probabilistic Description of Risks; 1.2.1 Probability space; 1.2.2 Experiment and universe; 1.2.3 Random events; 1.2.4 Sigma-algebra; 1.2.5 Probability measure; 1.3 Independence for Events and Conditional Probabilities; 1.3.1 Independent events; 1.3.2 Conditional probability; 1.4 Random Variables and Random Vectors; 1.4.1 Random variables; 1.4.2 Random vectors; 1.4.3 Risks and losses; 1.5 Distribution Functions; 1.5.1 Univariate distribution functions ; 1.5.2 Multivariate distribution functions1.5.3 Tail functions; 1.5.4 Support; 1.5.5 Discrete random variables; 1.5.6 Continuous random variables; 1.5.7 General random variables; 1.5.8 Quantile functions; 1.5.9 Independence for random variables; 1.6 Mathematical Expectation; 1.6.1 Construction; 1.6.2 Riemann-Stieltjes integral; 1.6.3 Law of large numbers; 1.6.4 Alternative representations for the mathematical expectation in the continuous case; 1.6.5 Alternative representations for the mathematical expectation in the discrete case; 1.6.6 Stochastic Taylor expansion ; 1.6.7 Variance and covariance1.7 Transforms; 1.7.1 Stop-loss transform; 1.7.2 Hazard rate; 1.7.3 Mean-excess function; 1.7.4 Stationary renewal distribution; 1.7.5 Laplace transform; 1.7.6 Moment generating function; 1.8 Conditional Distributions; 1.8.1 Conditional densities; 1.8.2 Conditional independence; 1.8.3 Conditional variance and covariance; 1.8.4 The multivariate normal distribution; 1.8.5 The family of the elliptical distributions; 1.9 Comonotonicity; 1.9.1 Definition; 1.9.2 Comonotonicity and Fréchet upper bound; 1.10 Mutual Exclusivity; 1.10.1 Definition ; 1.10.2 Fréchet lower bound1.10.3 Existence of Fréchet lower bounds in Fréchet spaces; 1.10.4 Fréchet lower bounds and maxima; 1.10.5 Mutual exclusivity and Fréchet lower bound; 1.11 Exercises; 2 Measuring Risk; 2.1 Introduction; 2.2 Risk Measures; 2.2.1 Definition; 2.2.2 Premium calculation principles; 2.2.3 Desirable properties; 2.2.4 Coherent risk measures; 2.2.5 Coherent and scenario-based risk measures; 2.2.6 Economic capital; 2.2.7 Expected risk-adjusted capital; 2.3 Value-at-Risk; 2.3.1 Definition; 2.3.2 Properties; 2.3.3 VaR-based economic capital ; 2.3.4 VaR and the capital asset pricing model2.4 Tail Value-at-Risk; 2.4.1 Definition; 2.4.2 Some related risk measures; 2.4.3 Properties; 2.4.4 TVaR-based economic capital; 2.5 Risk Measures Based on Expected Utility Theory; 2.5.1 Brief introduction to expected utility theory; 2.5.2 Zero-Utility Premiums; 2.5.3 Esscher risk measure; 2.6 Risk Measures Based on Distorted Expectation Theory; 2.6.1 Brief introduction to distorted expectation theory; 2.6.2 Wang risk measures; 2.6.3 Some particular cases of Wang risk measures; 2.7 Exercises; 2.8 Appendix: Convexity and Concavity; 2.8.1 Definition ; 2.8.2 Equivalent conditions
• Sommario/riassunto: 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
• Titolo autorizzato: Actuarial theory for dependent risks
• ISBN: 1-280-44873-3; 9786610448739; 0-470-01645-0; 0-470-01644-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910143705203321
• Lo trovi qui: Univ. Federico II