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Paper details
Number 4 - December 2023
Volume 33 - 2023
Claim modeling and insurance premium pricing under a bonus-malus system in motor insurance
Weenakorn Ieosanurak, Banphatree Khomkham, Adisak Moumeesri
Abstract
Accurately modeling claims data and determining appropriate insurance premiums are vital responsibilities for non-life
insurance firms. This article presents novel models for claims that offer improved precision in fitting claim data, both
in terms of claim frequency and severity. Specifically, we suggest the Poisson-GaL distribution for claim frequency and
the exponential-GaL distribution for claim severity. The traditional method of assigning automobile premiums based on
a bonus-malus system relies solely on the number of claims made. However, this may lead to unfair outcomes when
an insured individual with a minor severity claim is charged the same premium as someone with a severe claim. The
second aim of this article is to propose a new model for calculating bonus-malus premiums. Our proposed model takes
into account both the number and size of claims, which follow the Poisson-GaL distribution and the exponential-GaL
distribution, respectively. To calculate the premiums, we employ the Bayesian approach. Real-world data are used in
practical examples to illustrate how the proposed model can be implemented. The results of our analysis indicate that the
proposed premium model effectively resolves the issue of overcharging. Moreover, the proposed model produces premiums
that are more tailored to policyholders’ claim histories, benefiting both the policyholders and the insurance companies. This
advantage can contribute to the growth of the insurance industry and provide a competitive edge in the insurance market.
Keywords
bonus-malus system, claim severity, exponential-GaL distribution, motor insurance, number of claims, Poisson-GaL distribution