A Review of Bayesian Asymptotics in General Insurance Applications

Abstract

Over the last two decades, Bayesian methods have been widely used in general insurance applications, ranging from credibility theory to loss-reserves estimation, but this literature rarely addresses questions about the method's asymptotic properties. In this paper, we review the Bayesian's notion of posterior consistency in both parametric and nonparametric models and its implication on the sensitivity of the posterior to the actuary's choice of prior. We review some of the techniques for proving posterior consistency and, for illustration, we apply these results to investigate the asymptotic properties of several recently proposed Bayesian methods in general insurance.

Keywords: General insurance; nonparametric Bayes; posterior consistency; posterior robustness; property and casualty insurance

JEL Classification: C11; G22