On the use of MCMC simulation for stochastic reserving

In this paper we explore the use of Markov chain Monte Carlo (MCMC) simulation in stochastic reserving under Australian regulatory environment. We apply two sets of Bayesian models within the framework of generalised linear models (GLMs) to some claims run-off data (gross of reinsurance) of two lines of business and use the software WinBUGS (Bayesian Inference Using Gibbs Sampling) to carry out MCMC simulation. This simulation procedure is capable of producing the entire distribution and is a useful tool for determining different percentiles for risk margin, security loading, and risk management purposes. While the previous papers on Bayesian MCMC reserving generally do not examine the residuals after model fitting, here we adopt formal model criticism procedures to refine and validate the model structures tested. We also perform convergence and autocorrelation tests on the simulated samples. We find that our final models are able to incorporate particular features of the data and produce reasonable results in general. We also compare our estimates with the industry risk margin levels.