Allowing for time and cross dependence assumptions between claim counts in ratemaking models

Abstract

For purposes of ratemaking, time dependence and cross dependence have been treated as separate entities in the actuarial literature. Indeed, to date, little attention has been paid to the possibility of considering the two together. To discuss the effect of the simultaneous inclusion of different dependence assumptions in ratemaking models, a bivariate INAR(1) regression model is adapted to the ratemaking problem of pricing an automobile insurance contract with two types of coverage, taking into account both the correlation between claims from different coverage types and the serial correlation between the observations of the same policyholder observed over time. A numerical application using an automobile insurance claims database is conducted and the main finding is that the improvement obtained with a BINAR(1) regression model, compared to the outcomes of the simplest models, is marked, implying that we need to consider both time and cross correlations to fit the data at hand. In addition, the BINAR(1) specification shows a third source of dependence to be significant, namely, cross-time dependence.