ANALYSIS OF THE BONUS SYSTEM IN INSURANCE USING MARKOV CHAINS

Abstract

One of the ways in the insurance premium calculation procedure is to determine the premium based on experience. A significant role belongs to the so-called bonus system in practical examples of determining the number of insurance premiums. The procedure for applying this system is based on the previous compensation claims analysis, in the operationalization of which the application of Markov chains occupies a pivotal place. The goal is to show and point out the importance of Markov processes and one of the segments of their application in an appropriate way, which in this case is the insurance field. This paper deals with the bonus system used in motor vehicle insurance. Insurance users fall into three discount categories, and an analysis of the number of future premiums was performed depending on the damages incurred and the probability of their reporting. It has been shown that there may be a disproportion between the current amounts of premiums to be paid and the amounts of reported claims. This situation arises due to the small number of discount categories and slight differences in discount levels. The paper also discusses the possibility of analyzing future premiums depending on the damage done and the probability of its reporting in particular cases of an insured individual.