Stochastic Claims Reserving Methods in Insurance

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 Buhlmann-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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