Stochastic claims reserving methods in insurance [[electronic resource] /] / Mario V. Wüthrich and Michael Merz

• Autore: Wüthrich Mario V
• Pubblicazione: Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2008
• Descrizione fisica: 1 online resource (440 p.)
• Disciplina: 368/.0140151922
• Soggetto topico: Insurance claims - Mathematical models; Assegurances; Models matemàtics
• Soggetto genere / forma: Llibres electrònics
• Altri autori: MerzMichael
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [409]-415) and index.
• Nota di contenuto: Stochastic Claims Reserving Methods in Insurance; Contents; Preface; Acknowledgement; 1 Introduction and Notation; 1.1 Claims process; 1.1.1 Accounting principles and accident years; 1.1.2 Inflation; 1.2 Structural framework to the claims-reserving problem; 1.2.1 Fundamental properties of the claims reserving process; 1.2.2 Known and unknown claims; 1.3 Outstanding loss liabilities, classical notation; 1.4 General remarks; 2 Basic Methods; 2.1 Chain-ladder method (distribution-free); 2.2 Bornhuetter-Ferguson method; 2.3 Number of IBNyR claims, Poisson model ; 2.4 Poisson derivation of the CL algorithm3 Chain-Ladder Models; 3.1 Mean square error of prediction; 3.2 Chain-ladder method; 3.2.1 Mack model (distribution-free CL model); 3.2.2 Conditional process variance; 3.2.3 Estimation error for single accident years; 3.2.4 Conditional MSEP, aggregated accident years; 3.3 Bounds in the unconditional approach; 3.3.1 Results and interpretation; 3.3.2 Aggregation of accident years; 3.3.3 Proof of Theorems 3.17, 3.18 and 3.20; 3.4 Analysis of error terms in the CL method; 3.4.1 Classical CL model; 3.4.2 Enhanced CL model; 3.4.3 Interpretation ; 3.4.4 CL estimator in the enhanced model3.4.5 Conditional process and parameter prediction errors; 3.4.6 CL factors and parameter estimation error; 3.4.7 Parameter estimation; 4 Bayesian Models; 4.1 Benktander-Hovinen method and Cape-Cod model; 4.1.1 Benktander-Hovinen method; 4.1.2 Cape-Cod model; 4.2 Credible claims reserving methods; 4.2.1 Minimizing quadratic loss functions; 4.2.2 Distributional examples to credible claims reserving; 4.2.3 Log-normal/Log-normal model; 4.3 Exact Bayesian models; 4.3.1 Overdispersed Poisson model with gamma prior distribution ; 4.3.2 Exponential dispersion family with its associated conjugates4.4 Markov chain Monte Carlo methods; 4.5 Bühlmann-Straub credibility model; 4.6 Multidimensional credibility models; 4.6.1 Hachemeister regression model; 4.6.2 Other credibility models; 4.7 Kalman filter; 5 Distributional Models; 5.1 Log-normal model for cumulative claims; 5.1.1 Known variances 2j; 5.1.2 Unknown variances; 5.2 Incremental claims; 5.2.1 (Overdispersed) Poisson model; 5.2.2 Negative-Binomial model; 5.2.3 Log-normal model for incremental claims; 5.2.4 Gamma model; 5.2.5 Tweedie's compound Poisson model ; 5.2.6 Wright's model6 Generalized Linear Models; 6.1 Maximum likelihood estimators; 6.2 Generalized linear models framework; 6.3 Exponential dispersion family; 6.4 Parameter estimation in the EDF; 6.4.1 MLE for the EDF; 6.4.2 Fisher's scoring method; 6.4.3 Mean square error of prediction; 6.5 Other GLM models; 6.6 Bornhuetter-Ferguson method, revisited; 6.6.1 MSEP in the BF method, single accident year; 6.6.2 MSEP in the BF method, aggregated accident years; 7 Bootstrap Methods; 7.1 Introduction; 7.1.1 Efron's non-parametric bootstrap; 7.1.2 Parametric bootstrap ; 7.2 Log-normal model for cumulative sizes
• Sommario/riassunto: Claims reserving is central to the insurance industry. Insurance liabilities depend on a number of different risk factors which need to be predicted accurately. This prediction of risk factors and outstanding loss liabilities is the core for pricing insurance products, determining the profitability of an insurance company and for considering the financial strength (solvency) of the company.Following several high-profile company insolvencies, regulatory requirements have moved towards a risk-adjusted basis which has lead to the Solvency II developments. The key focus in the new regi
• Titolo autorizzato: Stochastic claims reserving methods in insurance
• ISBN: 1-119-20626-X; 1-282-35012-9; 9786612350122; 0-470-77272-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910146099603321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley finance series.