Bonus/Malus System in Pricing Compulsory Traffic Insurance According to The Negative Binomial Distribution

The bonus/malus system produces results by providing reduction or increase in premiums for the current year, considering the insured's losses in the past years. The system, which depends on the determination of the suitability of past claims data to a probability distribution the premiums of the insured, has the aim of obtaining fair premiums and directing them towards more careful vehicle driving. The aim of study is to determine the bonus/malus premiums of compulsory traffic insurances in Turkey based on negative binomial distribution. For this purpose, the study tries to establish the results of a fair bonus/malus system according to the damage numbers of insured. Firstly, the bonus/malus system is explained. Subsequently, the system and negative binomial distribution are described. In the application section, the real damage numbers of the compulsory traffic insurance for 2015 were used. Then, the suitability of the data set to the negative binomial distribution was examined. In the last part, a system was established and the results indicating fair premium amounts varying according to the damage numbers have been obtained. Finally, it has been found the malus increases in the premium changes compared to the previous year are higher than the bonus increases