Abstract

This thesis develops an alternative approach to modelling the expected loss cost of an insurance portfolio that allows for dependence between the frequency and severity components of the aggregate claims process. The traditionally used independent aggregate claims model is extended to define a dependent model, thus allowing for a correlation between the claim counts and claim amounts. A Generalized Linear Model framework is developed for the aggregate claims model in the dependent setting using a conditional severity model and marginal frequency model. We find that the pure premium in the dependent aggregate claims model is the product of a marginal mean frequency, a modified marginal mean severity and a correction term. This dependent modelling approach is then compared with the independent aggregate claims model GLM structure. It is shown that the expected total loss amount derived in the independent model is in fact a special case of the dependent model.