Abstract:
This research aims to develop a motor vehicle insurance premium
calculation model using the Bonus Malus system (BMS) that adjusts premiums
based on the policyholder's claim history. This system provides a bonus (premium
decrease) if there is no claim and malus (premium increase) if there is a claim.
The research modeled the frequency of claims with a Poisson-Gamma Lindley
(GaL) distribution and the severity of claims with a Lognormal-Gamma
distribution, using a Bayesian approach to produce fairer and more accurate
premiums. The data used came from 2004-2005 motor vehicle insurance policies
at Macquarie University, Australia, with a total of 67,856 policies and 4,624
claims. Distribution fit tests confirmed that the claim frequency data fit the
Poisson-GaL distribution (Chi-Square test statistic: 1.150 < 5.991) and the claim
severity data fit the Lognormal-Gamma distribution (Anderson-Darling test
statistic: 0.399 < 2.492). Parameter estimation using Maximum Likelihood
Estimation (MLE) resulted in parameter values for Poisson-GaL (�㔃 = 18.553; Ā =
1.460) and Lognormal-Gamma (Ā = 6.956; Ā = 9.996; ÿ = 10.293). The results
showed that the initial premium without a claim was $ 127.77. If the policyholder
makes a claim in the first year, the premium increases to $ 225.37, while without a
claim, the premium drops to $ 120.17. This system promotes premium fairness
based on individual risk profiles, optimizes the financial stability of insurance
companies, and motivates responsible behavior. Recommendations for future
research include considering external factors such as government policies and
applying the model to data from different regions or periods for broader
validation.
