Optimal Bonus-Malus System Design in Motor Third-Party Liability Insurance in Turkey: Negative Binomial Model

Abstract

One of the most significant instruments used in motor third-party liability insurance rating is bonus-malus system. The aim of the bonus-malus system is to provide a fairness of the premiums paid by ensuring everyone pays a premium that corresponds exactly to their own claim frequency. A balance of total amount of bonuses and maluses is very important to maintain the financial stability of the insurance companies. In Turkey, free tariff regime in motor third-party liability insurance has been adopted since 2014. In this study, an experience rating was employed via the insured’s individual claim experience by considering the drawbacks of using mandatory bonus-malus system. Data entailing information about the claim frequencies of automobiles over a year for motor third party liability policies were obtained from an insurance company. Optimal bonus-malus rates are determined by negative binomial model by using credibility theory, Bayesian approach and the principle of expected value premium.