Comparison of stochastic reserving methods

ISBN 07340 3570 5This paper compares several stochastic reserving methods on both qualitative and quantitative aspects in dealing with the outstanding claims liabilities. These methods include Bayesian estimation with Markov chain Monte Carlo (MCMC) simulation, the chain ladder method with bootstrapping, generalised linear models (GLMs) with bootstrapping, the Kalman filter on state-space models, the Mack model, and the stochastic chain ladder method. To start with, the outline of this paper and different types of uncertainty are set forth in Sections 1 and 2. The notation and terminology are stated in Section 3. The strengths and limitations of the methods are examined by considering the underlying structures, assumptions, and estimation mechanics, in Sections 4 to 10. The application of each method is then tested on a particular claims data set in Section 11, similar to the analysis in Mack (1993a). Conclusions are presented in Section 12. This paper is an excerpt of the author’s PhD thesis.All the calculations were done on Excel spreadsheets with VBA (Visual Basic for Applications) coding and the software BUGS (Bayesian Inference Using Gibbs Sampling). When large amounts of simulation were carried out in the analysis, approximation formulae were used to provide reasonable checks. In addition, some proofs and derivations are stated in the appendices for reference purposes. Details regarding the use of VBA and BUGS codings can be provided upon request to the author