LEADER 05187nam 22005894a 450 001 9910830595403321 005 20230617040710.0 010 $a1-280-44873-3 010 $a9786610448739 010 $a0-470-01645-0 010 $a0-470-01644-2 035 $a(CKB)1000000000357388 035 $a(EBL)257676 035 $a(SSID)ssj0000096991 035 $a(PQKBManifestationID)11120016 035 $a(PQKBTitleCode)TC0000096991 035 $a(PQKBWorkID)10083688 035 $a(PQKB)11615975 035 $a(MiAaPQ)EBC257676 035 $a(OCoLC)85820815 035 $a(EXLCZ)991000000000357388 100 $a20050318d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aActuarial theory for dependent risks$b[electronic resource] $emeasures, orders and models /$fM. Denuit ... [et al.] 210 $aHoboken, N.J. $cWiley$dc2005 215 $a1 online resource (460 p.) 300 $aDescription based upon print version of record. 311 $a0-470-01492-X 320 $aIncludes bibliographical references p. ([422]-437) and index. 327 $aActuarial 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 327 $a1.5.2 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 327 $a1.6.7 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 Fre?chet upper bound; 1.10 Mutual Exclusivity; 1.10.1 Definition 327 $a1.10.2 Fre?chet lower bound1.10.3 Existence of Fre?chet lower bounds in Fre?chet spaces; 1.10.4 Fre?chet lower bounds and maxima; 1.10.5 Mutual exclusivity and Fre?chet 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 327 $a2.3.4 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 327 $a2.8.2 Equivalent conditions 330 $aThe 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 606 $aRisk (Insurance)$xMathematical models 615 0$aRisk (Insurance)$xMathematical models. 676 $a368 676 $a368/.001/51 701 $aDenuit$b M$g(Michel)$0781288 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830595403321 996 $aActuarial theory for dependent risks$94028179 997 $aUNINA