Predictive Claim Scores for Dynamic Multi-Product Risk Classification in Insurance

It has become standard practice in the non-life insurance industry to employ Generalized Linear Models (GLMs) for insurance pricing. However, these GLMs traditionally work only with a priori characteristics of policyholders, while nowadays we increasingly have a posteriori information of individual customers available, sometimes even across multiple product categories. In this paper, we therefore consider a dynamic claim score to capture this a posteriori information over several product lines. More specifically, we extend the Bonus-Malus-panel model of Boucher and Inoussa (2014) and Boucher and Pigeon (2018) to include claim scores from other product categories and to allow for non-linear effects of these scores. The application of the resulting multi-product framework to a Dutch property and casualty insurance portfolio shows that the claims experience of individual customers can have a significant impact on the risk classification and that it can be very profitable to account for it.