Chain Ladder Method: Bayesian Bootstrap versus Classical Bootstrap

The intention of this paper is to analyse the mean square error of prediction (MSEP) under the distribution-free chain ladder (DFCL) claims reserving method. We compare the estimation obtained from the classical bootstrap method with the one obtained from a Bayesian bootstrap. To achieve this in the DFCL model we develop a novel approximate Bayesian computation (ABC) sampling algorithm to obtain the empirical posterior distribution. We need an ABC sampling algorithm because we work in a distribution-free setting. The use of this ABC methodology combined with bootstrap allows us to obtain samples from the intractable posterior distribution without the requirement of any distributional assumptions. This then enables us to calculate the MSEP and other risk measures like Value-at-Risk.