  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.
