Sequential Monte Carlo samplers to fit and compare insurance loss models

Abstract

Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the ‘body’ and the other for the ‘tail’ of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset.