Bonus-Malus Systems with Hybrid Claim Severity Distributions

One of the pricing strategies for Bonus-Malus (BM) systems relies on the decomposition of the claims’ randomness, namely, one part accounting for claims’ frequency and the other part for claims’ severity. For a Negative Binomial number of claims, we focused on the modelling of claim severities using a hybrid structure. While Weibull distribution is suggested for constructing smaller-sized claims, Pareto severities employed by (1) were applied to model large ones. A generalised function for the BM premium rates is then derived. Results are illustrated by a numerical example.