Dispersion modelling of outstanding claims with double Poisson regression models

Over-dispersed Poisson chain-ladder models are widely used in general insurance claims reserving. Although such models can accommodate the over-dispersion frequently observed in run-off triangles, they also impose an additional constraint of fixed variance to mean ratio across cells. In this paper, we relax this constraint and develop a flexible dispersion structure in a double Poisson chain-ladder model. The proposed model nests the classic over-dispersed Poisson model as a special case. A generalized likelihood ratio test is further proposed to compare different dispersion structures. In contrast to the existing claims reserving methods, our proposed method is more flexible in terms of the dispersion modelling. Simulation and empirical studies are conducted to demonstrate the importance of flexible dispersion modelling.