Note on mismodelling of policyholder's age in claim frequency model: A matter of gender in vehicle insurance

Abstract

Using the motor hull insurance data of Czech insurer, the paper deals with how mismodelling of policyholder's age can induce misleading conclusions about the gender differences in claim frequency within vehicle insurance. This study is based on individual data with unit policy duration and puts the emphasis on correct modelling of functional form of the age to show that mismodelling as well as categorization yields misleading conclusions and, finally, we demonstrate how the inferences depend on categorization itself. Thus, we showed that linear form as well as the categorization increases the type I error to detect the obvious interaction between gender and age. By involving fractional polynomials, the results partially support the judgement of European Court of Justice to ban using gender as a rating factor, in particular for young policyholders. We concluded that, if another relevant data are not available, the gender as well as interaction with the age should be considered in the claim frequency model although such model cannot be used for setting premium.