Experience rating in the Cramér-Lundberg model

Abstract

This paper provides a study of how experience rating on both claim frequency and severity impacts the solvency of an insurance business in the continuous-time Cramér Lundberg model. This is done by treating the claim parameters as random outcomes and continuously updating the premiums using Bayesian estimators. In the analysis, the claim sizes conditional on the severity parameter are assumed to be light-tailed. The main contributions are large deviation results where the asymptotic ruin probability is found for a model updating the premium based upon both frequency and severity. This asymptotic ruin probability is lower and decays faster compared to the one of a model which updates the premium solely based on claim frequency. Our findings are illustrated with examples, where the conditional claim size and the severity parameter are parametrised.