The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters

We introduce a multivariate Poisson-Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson-Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson-Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation-Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance.