On the use of conditional specification models in claim count distributions: an application to bonus-malus system

Abstract

In this paper a new methodology using the conditional specification technique introduced by Arnold et al. (1999) is used to obtain bonus-malus premiumns. A Poisson distribution for wich the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, a s a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas.