Actuarial modelling of claim counts [[electronic resource] ] : risk classification, credibility and bonus-malus systems / / Michel Denuit ... [et al.]

• Pubblicazione: Chichester, West Sussex, England ; ; Hoboken, NJ, : Wiley, c2007
• Descrizione fisica: 1 online resource (386 p.)
• Disciplina: 368.092; 368.092094
• Soggetto topico: Automobile insurance - Rates - Europe; Automobile insurance claims - Europe
• Altri autori: DenuitM (Michel)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [345]-353) and index.
• 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
• Sommario/riassunto: There are a wide range of variables for actuaries to consider when calculating a motorist's insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists' rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account e
• Titolo autorizzato: Actuarial modelling of claim counts
• ISBN: 1-280-97406-0; 9786610974061; 0-470-51742-5; 0-470-51741-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910841108603321
• Lo trovi qui: Univ. Federico II