Ranking and classification of automobile insurance policies according to the number of claims

In the ratemaking process, the ranking which takes into account the number of claims generated by a policy in a given period of insurance, may be helpful. For example, such a ranking allows to classify the newly concluded insurance policy to the appropriate tariff groups and to differentiate policies with no claims observed in the insurance history. For this purpose, in this paper we analyze models applicable to the modeling of count variables. In the first part of the paper, we present the classical Poisson regression and a modified regression model for data, where there is a large number of zeros in the values of the counter variable, which is a common situation in the insurance data. In the second part, we expand the classical Poisson regression by adding the random effect. The goal is to avoid an unrealistic assumption that in every class all insurance policies are characterized by the same expected number of claims. In the last part of the paper, we propose to use k-fold cross-validation to identify the factors which influence the number of insurance claims the most. Then, setting the parameters of the Poisson distribution, we create the ranking of policies using the estimated parameters of the model, which give the smallest cross-validation mean squared error. In the paper we use a real-world data set taken from literature. For all computations we used the free software environment R.