Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this oft unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. This model is both easy to implement and has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium can be expressed as the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpretable correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset.
Published December 2015 , 17 pages