A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component

The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.