Stochastic Loss Reserving Using Bayesian MCMC Models

The emergence of Bayesian Markov Chain Monte-Carlo (MCMC) models has provided actuaries with an unprecedented flexibility in stochastic model development. Another recent development has been the posting of a database on the CAS website that consists of hundreds of loss development triangles with outcomes. This monograph begins by first testing the performance of the Mack model on incurred data, and the Bootstrap Overdispersed Poisson model on paid data. It then will identify features of some Bayesian MCMC models that improve the performance over the above models. The features examined include (1) recognizing correlation between accident years; (2) introducing a skewed distribution defined over the entire real line to deal with negative incremental paid data; (3) allowing for a payment year trend on paid data; and (4) allowing for a change in the claim settlement rate. While the specific conclusions of this monograph pertain only to the data in the CAS Loss Reserve Database, the breadth of this study suggests that the currently popular models might similarly understate the range of outcomes for other loss triangles. This monograph then suggests features of models that actuaries might consider implementing in their stochastic loss reserve models to improve their estimates of the expected range of outcomes.

Keywords: Reserving, Loss Reserving, Bootstrapping, Bayesian Models