Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains di®erent types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce di®erent multivariate Poisson regression models in order to relax the independence assumption, including zero-in°ated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three di®erent types of claims. We analyse the consequences for pure and loaded pre- miums when the independence assumption is relaxed by using di®erent multivariate Poisson regression models and their zero-in°ated versions.