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Author Merz, Michael
Title Stochastic Claims Reserving Methods in Insurance : Reserving Methods in Insurance
Imprint Hoboken : John Wiley & Sons, Incorporated, 2008
©2008
book jacket
Edition 1st ed
Descript 1 online resource (440 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series The Wiley Finance Ser. ; v.435
The Wiley Finance Ser
Note 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 algorithm -- 3 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 model -- 3.4.5 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 conjugates -- 4.4 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 model -- 6 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 -- 7.3 Generalized linear models -- 7.4 Chain-ladder method -- 7.4.1 Approach 1: Unconditional estimation error -- 7.4.2 Approach 3: Conditional estimation error -- 7.5 Mathematical thoughts about bootstrapping methods -- 7.6 Synchronous bootstrapping of seemingly unrelated regressions -- 8 Multivariate Reserving Methods -- 8.1 General multivariate framework -- 8.2 Multivariate chain-ladder method -- 8.2.1 Multivariate CL model -- 8.2.2 Conditional process variance -- 8.2.3 Conditional estimation error for single accident years -- 8.2.4 Conditional MSEP, aggregated accident years
8.2.5 Parameter estimation -- 8.3 Multivariate additive loss reserving method -- 8.3.1 Multivariate additive loss reserving model -- 8.3.2 Conditional process variance -- 8.3.3 Conditional estimation error for single accident years -- 8.3.4 Conditional MSEP, aggregated accident years -- 8.3.5 Parameter estimation -- 8.4 Combined Multivariate CL and ALR method -- 8.4.1 Combined CL and ALR method: the model -- 8.4.2 Conditional cross process variance -- 8.4.3 Conditional cross estimation error for single accident years -- 8.4.4 Conditional MSEP, aggregated accident years -- 8.4.5 Parameter estimation -- 9 Selected Topics I: Chain-Ladder Methods -- 9.1 Munich chain-ladder -- 9.1.1 The Munich chain-ladder model -- 9.1.2 Credibility approach to the MCL method -- 9.1.3 MCL Parameter estimation -- 9.2 CL Reserving: A Bayesian inference model -- 9.2.1 Prediction of the ultimate claim -- 9.2.2 Likelihood function and posterior distribution -- 9.2.3 Mean square error of prediction -- 9.2.4 Credibility chain-ladder -- 9.2.5 Examples -- 9.2.6 Markov chain Monte Carlo methods -- 10 Selected Topics II: Individual Claims Development Processes -- 10.1 Modelling claims development processes for individual claims -- 10.1.1 Modelling framework -- 10.1.2 Claims reserving categories -- 10.2 Separating IBNeR and IBNyR claims -- 11 Statistical Diagnostics -- 11.1 Testing age-to-age factors -- 11.1.1 Model choice -- 11.1.2 Age-to-age factors -- 11.1.3 Homogeneity in time and distributional assumptions -- 11.1.4 Correlations -- 11.1.5 Diagonal effects -- 11.2 Non-parametric smoothing -- Appendix A: Distributions -- A.1 Discrete distributions -- A.1.1 Binomial distribution -- A.1.2 Poisson distribution -- A.1.3 Negative-Binomial distribution -- A.2 Continuous distributions -- A.2.1 Uniform distribution -- A.2.2 Normal distribution -- A.2.3 Log-normal distribution
A.2.4 Gamma distribution -- A.2.5 Beta distribution -- Bibliography -- Index
"It is astonishing that the methods used for claims reserving in non life-insurance are, even still today, driven by a deterministic understanding of one or several computational algorithms. Stochastic Claims Reserving Methods in Insurance is tremendously widening this traditional understanding. In this text reserving is model driven, computational algorithms become a consequence of the chosen model. Only with this approach it makes sense to ask how predicted reserves might vary. Stochastic reserving is hence the corner stone of successful risk management for the technical result of an insurance company. Mario Wüthrich and Michael Merz have to be congratulated for opening the eyes of the non-life-actuary to a new and modern dimension." -Hans Bühlmann, Swiss Federal Institute of Technology, Zurich "Assessing the best estimate of insurance liabilities and modelling their adverse developments are among the new frontiers of insurance under the new IAS and the proposed new solvency regimes. This book makes a leap towards these frontiers. The variegated issue of predicting outstanding loss liabilities in non-life insurance is addressed using the unified framework of theory of stochastic processes. The proposed approach provides valuable tools for tackling one of the most challenging forecasting problems in insurance." -Franco Moriconi, Professor of Finance, University of Perugia
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Merz, Michael Stochastic Claims Reserving Methods in Insurance : Reserving Methods in Insurance Hoboken : John Wiley & Sons, Incorporated,c2008 9780470723463
Subject Insurance claims -- Mathematical models
Electronic books
Alt Author Wüthrich, Mario V
Wuthrich, Mario
Wuthrich, Mario V
Wthrich, Mario V
Wü Thrich, Mario V
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