A Dynamic Bonus-Malus System for the Automobile Insurance : A Case Study in Iranian Third Party Liability

The classical Bonus-Malus System (BMS) determines the next year level of a policyholder based upon his/her current level along with the number of his/her claims during the current period. Moreover, such systems do not take into account other information, such as age, sex, etc., to determine the policyholder's level. This article employs the sophisticated Hidden Markov Model along with the ordinal logistic regression to introduce a Dynamic Bonus-Malus System (DBMS) which the policyholder's level considers as a hidden state. Then the exact level of a policyholder has been estimated by using the ordinal logistic regression model, which is developed based upon exactly collected observations along with negative binomial-inverse Gaussian distribution and the hidden Markov model. An application of such DMBS in Iranian automobile insurance has been given