Modeling risk premium of motor insurance usisng copula

Abstract

Risk premium is estimation of future claims on the basis of experience, where the experience will be available jar many groups over several time periods. Process of estimating the future claims involve modeling of two or more random variables. The joint behaviour modeling of the variables has often been based on independent assumptions. We believe that there are several practical cases where independence assumption in the claim estimates is not valid and the errors in analysis due to the independence assumption are unacceptable. A convenient way to express joint distributions of two or more random variables is provided by copula. This study presents some results in theory of the dependent between risks using copula, and the theory is applied on Malaysian Motor insurance risk premium. Statistical models are proposed for three components, corresponding to the frequency, type and severity of claims. The models are Poisson and negative binomial regression model for assessing claim frequency, multinomiallogit model 10 predict the type of insurance claim, whether it is third party injury, third party property damage, insured damage or some combination, and Gamma regression model to estimate amount of claim. The result of this study indicates that the dependence among different claim types is significant.