InhaltsangabePreface. Acknowledgement. 1 Introduction and Notation. 1.1 Claims Process. 1.2 Structural Framework to the Claims-Reserving Problem. 1.3 Outstanding Loss Liabilities, Classical Notation. 1.4 General Remarks. 2 Basic Methods. 2.1 ChainLadder Method (DistributionFree). 2.2 Bornhuetter-Ferguson Method. 2.3 Number of IBNyR Claims, Poisson Model. 2.4 Poisson Derivation of the CL Algorithm. 3 ChainLadder Models. 3.1 Mean Square Error of Prediction. 3.2 ChainLadder Method. 3.3 Bounds in the Unconditional Approach. 3.4 Analysis of Error Terms in the CL Method. 4 Bayesian Models. 4.1 Benktander-Hovinen Method and Cape-Cod Model. 4.2 Credible Claims Reserving Methods. 4.3 Exact Bayesian Models. 4.4 Markov Chain Monte Carlo Methods. 4.5 BühlmannStraub Credibility Model. 4.6 Multidimensional Credibility Models. 4.7 Kalman Filter. 5 Distributional Models. 5.1 LogNormal Model for Cumulative Claims. 5.2 Incremental Claims. 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. 6.5 Other GLM Models. 6.6 Bornhuetter-Ferguson Method, Revisited. 7 Bootstrap Methods. 7.1 Introduction. 7.2 LogNormal Model for Cumulative Sizes. 7.3 Generalized Linear Models. 7.4 ChainLadder Method. 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. 8.3 Multivariate Additive Loss Reserving Method. 8.4 Combined Multivariate CL and ALR Method. 9 Selected Topics I: Chain-Ladder Methods. 9.1 Munich Chain-Ladder. 9.2 CL Reserving: A Bayesian Inference Model. 10 Selected Topics II: Individual Claims Development Processes. 10.1 Modelling Claims Development Processes for Individual Claims. 10.2 Separating IBNeR and IBNyR Claims. 11 Statistical Diagnostics. 11.1 Testing Age-to-Age Factors. 11.2 NonParametric Smoothing. Appendix A: Distributions. A.1 Discrete Distributions. A.2 Continuous Distributions. Bibliography. Index.

Inhaltsangabe"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

Leseprobe

Preface. Acknowledgement. 1 Introduction and Notation. 1.1 Claims Process. 1.2 Structural Framework to the Claims-Reserving Problem. 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. 3.3 Bounds in the Unconditional Approach. 3.4 Analysis of Error Terms in the CL Method. 4 Bayesian Models. 4.1 Benktander-Hovinen Method and Cape-Cod Model. 4.2 Credible Claims Reserving Methods. 4.3 Exact Bayesian Models. 4.4 Markov Chain Monte Carlo Methods. 4.5 Bühlmann-Straub Credibility Model. 4.6 Multidimensional Credibility Models. 4.7 Kalman Filter. 5 Distributional Models. 5.1 Log-Normal Model for Cumulative Claims. 5.2 Incremental Claims. 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. 6.5 Other GLM Models. 6.6 Bornhuetter-Ferguson Method, Revisited. 7 Bootstrap Methods. 7.1 Introduction. 7.2 Log-Normal Model for Cumulative Sizes. 7.3 Generalized Linear Models. 7.4 Chain-Ladder Method. 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. 8.3 Multivariate Additive Loss Reserving Method. 8.4 Combined Multivariate CL and ALR Method. 9 Selected Topics I: Chain-Ladder Methods. 9.1 Munich Chain-Ladder. 9.2 CL Reserving: A Bayesian Inference Model. 10 Selected Topics II: Individual Claims Development Processes. 10.1 Modelling Claims Development Processes for Individual Claims. 10.2 Separating IBNeR and IBNyR Claims. 11 Statistical Diagnostics. 11.1 Testing Age-to-Age Factors. 11.2 Non-Parametric Smoothing. Appendix A: Distributions. A.1 Discrete Distributions. A.2 Continuous Distributions. Bibliography. Index.

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