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Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.]
| Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2005 |
| Descrizione fisica | 1 online resource (460 p.) |
| Disciplina |
368
368/.001/51 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico | Risk (Insurance) - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-44873-3
9786610448739 0-470-01645-0 0-470-01644-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910143705203321 |
| Hoboken, N.J., : Wiley, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.]
| Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2005 |
| Descrizione fisica | 1 online resource (460 p.) |
| Disciplina |
368
368/.001/51 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico | Risk (Insurance) - Mathematical models |
| ISBN |
1-280-44873-3
9786610448739 0-470-01645-0 0-470-01644-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910830595403321 |
| Hoboken, N.J., : Wiley, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.]
| Actuarial theory for dependent risks [[electronic resource] ] : measures, orders and models / / M. Denuit ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2005 |
| Descrizione fisica | 1 online resource (460 p.) |
| Disciplina |
368
368/.001/51 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico | Risk (Insurance) - Mathematical models |
| ISBN |
1-280-44873-3
9786610448739 0-470-01645-0 0-470-01644-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910840709903321 |
| Hoboken, N.J., : Wiley, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
