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<p>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.</p>
</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.

Claim Modeling and Insurance Premium Pricing Under A Bonus–Malus System in Motor Insurance

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Accurately modeling claims data and determining appropriate insurance premiums are vital responsibilities for non-life insurance firms. This article presents...

Claim Modeling and Insurance Premium Pricing Under A Bonus–Malus System in Motor Insurance

Published Online: Dec 21, 2023

Page range: 637 - 650

Received: Jun 10, 2023

Accepted: Sep 11, 2023

DOI: https://doi.org/10.34768/amcs-2023-0045

Keywords
bonus-malus system, claim severity, exponential-GaL distribution, motor insurance, number of claims, Poisson-GaL distribution

© 2023 Weenakorn Ieosanurak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Claim Modeling and Insurance Premium Pricing Under A Bonus–Malus System in Motor Insurance

Published Online: Dec 21, 2023

Page range: 637 - 650

Received: Jun 10, 2023

Accepted: Sep 11, 2023

DOI: https://doi.org/10.34768/amcs-2023-0045

Keywordsbonus-malus system, claim severity, exponential-GaL distribution, motor insurance, number of claims, Poisson-GaL distribution

© 2023 Weenakorn Ieosanurak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
bonus-malus system, claim severity, exponential-GaL distribution, motor insurance, number of claims, Poisson-GaL distribution