A proposed actuarial model for estimating the risk premium for vehicle insurance using central moments theory of claims

Abstract

This research aims to present an actuarial model for estimating the value at risk (VAR) for vehicle insurance, given the availability of a set of variables associated with determining this premium. These variables reflect both the driver's demographics and the vehicle model itself, and are based on an appropriate probability distribution for the number and value of vehicle insurance claims. Through the practical application of the proposed model, the article estimated the price limits for vehicle insurance rates at the company under study. It became clear that the rate used by the company deviates significantly from these limits, indicating a lack of consistency with the company's actual experience. The Gamma distribution is considered the appropriate distribution for claims values. The variables (age, vehicle age, policy term, and type) have a significant impact on claims values, while the remaining variables (vehicle value, education level, and marital status) have no significant impact on the study's response variable, which represents claims values. The results indicate that the total insurance rate at the company under study ranges between 7.22%, representing the minimum, and 7.48%, representing the maximum. Comparing this rate to the company's own rate of 9.87%, we find that it is higher than the company's experience. Therefore, it is necessary to reduce the insurance price to match its experience. The article recommended adopting the proposed pricing model, as practical application has proven that it reflects the actual experience of the company's data.