Bayesian Multivariate Mixed Poisson Models with Copula-Based Mixture

Abstract

It is common practice to use multivariate count modeling in actuarial literature when dealing with claim counts from insurance policies with multiple covers. One possible way to construct such a model is to implement copula directly on discrete margins. However, likelihood inference under this construction involves the computation of multidimensional rectangle probabilities, which could be computationally expensive, especially in the elliptical copula case. Another potential approach is based on the multivariate mixed Poisson model. The crucial work under this method is to find an appropriate multivariate continuous distribution for mixing parameters. By virtue of the copula, this issue coul..