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1: GLMs and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin
| 1: GLMs and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin |
| Autore | Denuit, Michel |
| Pubbl/distr/stampa | Cham, : Springer, 2019 |
| Descrizione fisica | xvi, 441 p. : ill. ; 24 cm |
| Altri autori (Persone) |
Hainaut, Donatien
Trufin, Julien |
| Soggetto topico |
68-XX - Computer science [MSC 2020]
62-XX - Statistics [MSC 2020] 62P05 - Applications of statistics to actuarial sciences and financial mathematics [MSC 2020] |
| Soggetto non controllato |
Exponential dispersion model
GLM Insurance risk classification Regression analysis Supervised learning |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0126842 |
Denuit, Michel
|
||
| Cham, : Springer, 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
1: GLMs and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin
| 1: GLMs and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin |
| Autore | Denuit, Michel |
| Edizione | [Cham : Springer, 2019] |
| Pubbl/distr/stampa | xvi, 441 p., : ill. ; 24 cm |
| Descrizione fisica | Pubblicazione in formato elettronico |
| Altri autori (Persone) |
Hainaut, Donatien
Trufin, Julien |
| Soggetto topico |
68-XX - Computer science [MSC 2020]
62-XX - Statistics [MSC 2020] 62P05 - Applications of statistics to actuarial sciences and financial mathematics [MSC 2020] |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0126842 |
|
Denuit, Michel
|
||
| xvi, 441 p., : ill. ; 24 cm | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
2: Tree-Based Methods and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin
| 2: Tree-Based Methods and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin |
| Autore | Denuit, Michel |
| Pubbl/distr/stampa | Cham, : Springer, 2020 |
| Descrizione fisica | x, 228 p. : ill. ; 24 cm |
| Altri autori (Persone) |
Hainaut, Donatien
Trufin, Julien |
| Soggetto topico |
62-XX - Statistics [MSC 2020]
68T05 - Learning and adaptive systems in artificial intelligence [MSC 2020] 62J12 - Generalized linear models (logistic models) [MSC 2020] 62M10 - Time series, auto-correlation, regression, etc. in statistics (GARCH) [MSC 2020] 91-XX - Game theory, economics, finance, and other social and behavioral sciences [MSC 2020] 62H30 - Classification and discrimination; cluster analysis (statistical aspects) [MSC 2020] 62P05 - Applications of statistics to actuarial sciences and financial mathematics [MSC 2020] 91G05 - Actuarial mathematics [MSC 2020] |
| Soggetto non controllato |
Actuarial modeling
Insurance risk classification Machine learning Supervised learning Tree-based methods for insurance |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0249059 |
|
Denuit, Michel
|
||
| Cham, : Springer, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
3: Neural Networks and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin
| 3: Neural Networks and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin |
| Autore | Denuit, Michel |
| Pubbl/distr/stampa | Cham, : Springer, 2019 |
| Descrizione fisica | xiii, 250 p. : ill. ; 24 cm |
| Altri autori (Persone) |
Hainaut, Donatien
Trufin, Julien |
| Soggetto topico |
68-XX - Computer science [MSC 2020]
62-XX - Statistics [MSC 2020] 62M45 - Neural nets and related approaches to inference from stochastic processes [MSC 2020] 62P05 - Applications of statistics to actuarial sciences and financial mathematics [MSC 2020] |
| Soggetto non controllato |
Actuarial modeling
Deep learing for insurance Insurance risk classification Machine learning Neural networks |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0126843 |
|
Denuit, Michel
|
||
| Cham, : Springer, 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
3: Neural Networks and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin
| 3: Neural Networks and Extensions / Michel Denuit, Donatien Hainaut, Julien Trufin |
| Autore | Denuit, Michel |
| Edizione | [Cham : Springer, 2019] |
| Pubbl/distr/stampa | xiii, 250 p., : ill. ; 24 cm |
| Descrizione fisica | Pubblicazione in formato elettronico |
| Altri autori (Persone) |
Hainaut, Donatien
Trufin, Julien |
| Soggetto topico |
68-XX - Computer science [MSC 2020]
62-XX - Statistics [MSC 2020] 62M45 - Neural nets and related approaches to inference from stochastic processes [MSC 2020] 62P05 - Applications of statistics to actuarial sciences and financial mathematics [MSC 2020] |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0126843 |
|
Denuit, Michel
|
||
| xiii, 250 p., : ill. ; 24 cm | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.]
| Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.] |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 |
| Descrizione fisica | 1 online resource (386 p.) |
| Disciplina |
368.092
368.092094 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico |
Automobile insurance - Rates - Europe
Automobile insurance claims - Europe |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-97406-0
9786610974061 0-470-51742-5 0-470-51741-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Actuarial Modelling of Claim Counts; Contents; Foreword; Preface; Notation; Part I Modelling Claim Counts; 1 Mixed Poisson Models for Claim Numbers; 1.1 Introduction; 1.1.1 Poisson Modelling for the Number of Claims; 1.1.2 Heterogeneity and Mixed Poisson Model; 1.1.3 Maximum Likelihood Estimation; 1.1.4 Agenda; 1.2 Probabilistic Tools; 1.2.1 Experiment and Universe; 1.2.2 Random Events; 1.2.3 Sigma-Algebra; 1.2.4 Probability Measure; 1.2.5 Independent Events; 1.2.6 Conditional Probability; 1.2.7 Random Variables and Random Vectors; 1.2.8 Distribution Functions
1.2.9 Independence for Random Variables1.3 Poisson Distribution; 1.3.1 Counting Random Variables; 1.3.2 Probability Mass Function; 1.3.3 Moments; 1.3.4 Probability Generating Function; 1.3.5 Convolution Product; 1.3.6 From the Binomial to the Poisson Distribution; 1.3.7 Poisson Process; 1.4 Mixed Poisson Distributions; 1.4.1 Expectations of General Random Variables; 1.4.2 Heterogeneity and Mixture Models; 1.4.3 Mixed Poisson Process; 1.4.4 Properties of Mixed Poisson Distributions; 1.4.5 Negative Binomial Distribution; 1.4.6 Poisson-Inverse Gaussian Distribution 1.4.7 Poisson-LogNormal Distribution1.5 Statistical Inference for Discrete Distributions; 1.5.1 Maximum Likelihood Estimators; 1.5.2 Properties of the Maximum Likelihood Estimators; 1.5.3 Computing the Maximum Likelihood Estimators with the Newton-Raphson Algorithm; 1.5.4 Hypothesis Tests; 1.6 Numerical Illustration; 1.7 Further Reading and Bibliographic Notes; 1.7.1 Mixed Poisson Distributions; 1.7.2 Survey of Empirical Studies Devoted to Claim Frequencies; 1.7.3 Semiparametric Approach; 2 Risk Classification; 2.1 Introduction; 2.1.1 Risk Classification, Regression Models and Random Effects 2.1.2 Risk Sharing in Segmented Tariffs2.1.3 Bonus Hunger and Censoring; 2.1.4 Agenda; 2.2 Descriptive Statistics for Portfolio A; 2.2.1 Global Figures; 2.2.2 Available Information; 2.2.3 Exposure-to-Risk; 2.2.4 One-Way Analyses; 2.2.5 Interactions; 2.2.6 True Versus Apparent Dependence; 2.3 Poisson Regression Model; 2.3.1 Coding Explanatory Variables; 2.3.2 Loglinear Poisson Regression Model; 2.3.3 Score; 2.3.4 Multiplicative Tariff; 2.3.5 Likelihood Equations; 2.3.6 Interpretation of the Likelihood Equations; 2.3.7 Solving the Likelihood Equations with the Newton-Raphson Algorithm 2.3.8 Wald Confidence Intervals2.3.9 Testing for Hypothesis on a Single Parameter; 2.3.10 Confidence Interval for the Expected Annual Claim Frequency; 2.3.11 Deviance; 2.3.12 Deviance Residuals; 2.3.13 Testing a Hypothesis on a Set of Parameters; 2.3.14 Specification Error and Robust Inference; 2.3.15 Numerical Illustration; 2.4 Overdispersion; 2.4.1 Explanation of the Phenomenon; 2.4.2 Interpreting Overdispersion; 2.4.3 Consequences of Overdispersion; 2.4.4 Modelling Overdispersion; 2.4.5 Detecting Overdispersion; 2.4.6 Testing for Overdispersion; 2.5 Negative Binomial Regression Model 2.5.1 Likelihood Equations |
| Record Nr. | UNINA-9910143586103321 |
| Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.]
| Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.] |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 |
| Descrizione fisica | 1 online resource (386 p.) |
| Disciplina |
368.092
368.092094 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico |
Automobile insurance - Rates - Europe
Automobile insurance claims - Europe |
| ISBN |
1-280-97406-0
9786610974061 0-470-51742-5 0-470-51741-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Actuarial Modelling of Claim Counts; Contents; Foreword; Preface; Notation; Part I Modelling Claim Counts; 1 Mixed Poisson Models for Claim Numbers; 1.1 Introduction; 1.1.1 Poisson Modelling for the Number of Claims; 1.1.2 Heterogeneity and Mixed Poisson Model; 1.1.3 Maximum Likelihood Estimation; 1.1.4 Agenda; 1.2 Probabilistic Tools; 1.2.1 Experiment and Universe; 1.2.2 Random Events; 1.2.3 Sigma-Algebra; 1.2.4 Probability Measure; 1.2.5 Independent Events; 1.2.6 Conditional Probability; 1.2.7 Random Variables and Random Vectors; 1.2.8 Distribution Functions
1.2.9 Independence for Random Variables1.3 Poisson Distribution; 1.3.1 Counting Random Variables; 1.3.2 Probability Mass Function; 1.3.3 Moments; 1.3.4 Probability Generating Function; 1.3.5 Convolution Product; 1.3.6 From the Binomial to the Poisson Distribution; 1.3.7 Poisson Process; 1.4 Mixed Poisson Distributions; 1.4.1 Expectations of General Random Variables; 1.4.2 Heterogeneity and Mixture Models; 1.4.3 Mixed Poisson Process; 1.4.4 Properties of Mixed Poisson Distributions; 1.4.5 Negative Binomial Distribution; 1.4.6 Poisson-Inverse Gaussian Distribution 1.4.7 Poisson-LogNormal Distribution1.5 Statistical Inference for Discrete Distributions; 1.5.1 Maximum Likelihood Estimators; 1.5.2 Properties of the Maximum Likelihood Estimators; 1.5.3 Computing the Maximum Likelihood Estimators with the Newton-Raphson Algorithm; 1.5.4 Hypothesis Tests; 1.6 Numerical Illustration; 1.7 Further Reading and Bibliographic Notes; 1.7.1 Mixed Poisson Distributions; 1.7.2 Survey of Empirical Studies Devoted to Claim Frequencies; 1.7.3 Semiparametric Approach; 2 Risk Classification; 2.1 Introduction; 2.1.1 Risk Classification, Regression Models and Random Effects 2.1.2 Risk Sharing in Segmented Tariffs2.1.3 Bonus Hunger and Censoring; 2.1.4 Agenda; 2.2 Descriptive Statistics for Portfolio A; 2.2.1 Global Figures; 2.2.2 Available Information; 2.2.3 Exposure-to-Risk; 2.2.4 One-Way Analyses; 2.2.5 Interactions; 2.2.6 True Versus Apparent Dependence; 2.3 Poisson Regression Model; 2.3.1 Coding Explanatory Variables; 2.3.2 Loglinear Poisson Regression Model; 2.3.3 Score; 2.3.4 Multiplicative Tariff; 2.3.5 Likelihood Equations; 2.3.6 Interpretation of the Likelihood Equations; 2.3.7 Solving the Likelihood Equations with the Newton-Raphson Algorithm 2.3.8 Wald Confidence Intervals2.3.9 Testing for Hypothesis on a Single Parameter; 2.3.10 Confidence Interval for the Expected Annual Claim Frequency; 2.3.11 Deviance; 2.3.12 Deviance Residuals; 2.3.13 Testing a Hypothesis on a Set of Parameters; 2.3.14 Specification Error and Robust Inference; 2.3.15 Numerical Illustration; 2.4 Overdispersion; 2.4.1 Explanation of the Phenomenon; 2.4.2 Interpreting Overdispersion; 2.4.3 Consequences of Overdispersion; 2.4.4 Modelling Overdispersion; 2.4.5 Detecting Overdispersion; 2.4.6 Testing for Overdispersion; 2.5 Negative Binomial Regression Model 2.5.1 Likelihood Equations |
| Record Nr. | UNINA-9910830911603321 |
| Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.]
| Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.] |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 |
| Descrizione fisica | 1 online resource (386 p.) |
| Disciplina |
368.092
368.092094 |
| Altri autori (Persone) | DenuitM (Michel) |
| Soggetto topico |
Automobile insurance - Rates - Europe
Automobile insurance claims - Europe |
| ISBN |
1-280-97406-0
9786610974061 0-470-51742-5 0-470-51741-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Actuarial Modelling of Claim Counts; Contents; Foreword; Preface; Notation; Part I Modelling Claim Counts; 1 Mixed Poisson Models for Claim Numbers; 1.1 Introduction; 1.1.1 Poisson Modelling for the Number of Claims; 1.1.2 Heterogeneity and Mixed Poisson Model; 1.1.3 Maximum Likelihood Estimation; 1.1.4 Agenda; 1.2 Probabilistic Tools; 1.2.1 Experiment and Universe; 1.2.2 Random Events; 1.2.3 Sigma-Algebra; 1.2.4 Probability Measure; 1.2.5 Independent Events; 1.2.6 Conditional Probability; 1.2.7 Random Variables and Random Vectors; 1.2.8 Distribution Functions
1.2.9 Independence for Random Variables1.3 Poisson Distribution; 1.3.1 Counting Random Variables; 1.3.2 Probability Mass Function; 1.3.3 Moments; 1.3.4 Probability Generating Function; 1.3.5 Convolution Product; 1.3.6 From the Binomial to the Poisson Distribution; 1.3.7 Poisson Process; 1.4 Mixed Poisson Distributions; 1.4.1 Expectations of General Random Variables; 1.4.2 Heterogeneity and Mixture Models; 1.4.3 Mixed Poisson Process; 1.4.4 Properties of Mixed Poisson Distributions; 1.4.5 Negative Binomial Distribution; 1.4.6 Poisson-Inverse Gaussian Distribution 1.4.7 Poisson-LogNormal Distribution1.5 Statistical Inference for Discrete Distributions; 1.5.1 Maximum Likelihood Estimators; 1.5.2 Properties of the Maximum Likelihood Estimators; 1.5.3 Computing the Maximum Likelihood Estimators with the Newton-Raphson Algorithm; 1.5.4 Hypothesis Tests; 1.6 Numerical Illustration; 1.7 Further Reading and Bibliographic Notes; 1.7.1 Mixed Poisson Distributions; 1.7.2 Survey of Empirical Studies Devoted to Claim Frequencies; 1.7.3 Semiparametric Approach; 2 Risk Classification; 2.1 Introduction; 2.1.1 Risk Classification, Regression Models and Random Effects 2.1.2 Risk Sharing in Segmented Tariffs2.1.3 Bonus Hunger and Censoring; 2.1.4 Agenda; 2.2 Descriptive Statistics for Portfolio A; 2.2.1 Global Figures; 2.2.2 Available Information; 2.2.3 Exposure-to-Risk; 2.2.4 One-Way Analyses; 2.2.5 Interactions; 2.2.6 True Versus Apparent Dependence; 2.3 Poisson Regression Model; 2.3.1 Coding Explanatory Variables; 2.3.2 Loglinear Poisson Regression Model; 2.3.3 Score; 2.3.4 Multiplicative Tariff; 2.3.5 Likelihood Equations; 2.3.6 Interpretation of the Likelihood Equations; 2.3.7 Solving the Likelihood Equations with the Newton-Raphson Algorithm 2.3.8 Wald Confidence Intervals2.3.9 Testing for Hypothesis on a Single Parameter; 2.3.10 Confidence Interval for the Expected Annual Claim Frequency; 2.3.11 Deviance; 2.3.12 Deviance Residuals; 2.3.13 Testing a Hypothesis on a Set of Parameters; 2.3.14 Specification Error and Robust Inference; 2.3.15 Numerical Illustration; 2.4 Overdispersion; 2.4.1 Explanation of the Phenomenon; 2.4.2 Interpreting Overdispersion; 2.4.3 Consequences of Overdispersion; 2.4.4 Modelling Overdispersion; 2.4.5 Detecting Overdispersion; 2.4.6 Testing for Overdispersion; 2.5 Negative Binomial Regression Model 2.5.1 Likelihood Equations |
| Record Nr. | UNINA-9910841108603321 |
| Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007 | ||
| 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 |
| 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 | ||
| ||
