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

Abstract

AbstractWe 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.