The goal of every insurance company is to assess a client as best as possible according to certain characteristics and then assign them a certain risk factor and adequate insurance premium. In order to achieve this, actuaries primarily use generalized linear models regardless of the insurance type. In car insurance companies, bonus-malus system of insurance is often used along with generalized linear models so as to ensure even further adjustment of the premium for each client. The application of the bonus-malus system has shown itself as necessary as actuaries are more often than not unable to ascertain drivers’ individual characteristics, e.g. reaction time and style of driving (aggressiveness, for example). Number of traffic accidents reported to the insurance company during the one-year period has proven to be an adequate substitute for the information on drivers’ individual characteristics.Bonus-malus system of insurance is founded on those premises, which means that the clients’ premiums are adjusted according to their previous claims during the year. As well as being very simple in its application, bonus-malus system is also important as it is a discrete-time Markov chain. Stationary distribution of Markov chain provides insurance companies with insight into the distribution of clients according to different premium degrees in the future, which allows them to calculate average premiums during the course of several years. In that way, an insurance company can estimate its revenue and adjust the premiums by classes, according to those estimations.