Uncertainty in heteroscedastic Bayesian model averaging

Abstract

The literature concerning liability evaluation is very well developed. It is however almost exclusively devoted to the performance of singular models. Recently, a variant of Bayesian Model Averaging (BMA) has been used for the first time to combine outstanding claims models. BMA is a widely used tool for model combination using Bayesian inference. Different versions of an expectation-maximisation (EM) algorithm are frequently used to apply BMA. This algorithm however has the issue of convergence to a single model. In this paper, we propose a numerical error integration approach to address the problem of convergence in a heteroscedastic context. We also generalise the proposed error integration approach by considering weights as a Dirichlet random variable, allowing for weights to vary. We compare the proposed approaches through simulation studies and a Property & Casualty insurance simulated dataset. We discuss some advantages of the proposed methods.