Conditional likelihood based inference on single-index models for motor Insurance claim severity

Abstract

Prediction of a traffic accident cost is one of the major problems in motor insurance. To identify the factors that influence costs is one of the main challenges of actuarial modelling. Telematics data about individual driving patterns could help calculating the expected claim severity in motor insurance. We propose using single-index models to assess the marginal effects of covariates on the claim severity conditional distribution. Thus, drivers with a claim cost distribution that has a long tail can be identified. These are risky drivers, who should pay a higher insurance premium and for whom preventative actions can be designed. A new kernel approach to estimate the covariance matrix of coefficients’ estimator is outlined. Its statistical properties are described and an application to an innovative data set containing information on driving styles is presented. The method provides good results when the response variable is skewed.