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Bonus-Malus Premiums Based on Claim Frequency and the Size of Claims

Author

Listed:
  • Adisak Moumeesri

    (Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Tippatai Pongsart

    (Department of Statistics, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

The bonus-malus system (BMS) is one of the most widely used tools in merit-rating automobile insurance, with the primary goal of ensuring that fair premiums are paid by all policyholders. The traditional BMS is dependent only on the claim frequency. Thus, an insured person who makes a claim with a small severity is penalized unfairly compared to an individual who makes a large severity claim. This study proposes a model for estimating the bonus-malus premium by employing a limit value (monetary unit) which distinguishes claim size into small and large based on claim frequency and claim severity distributions. This assists in determining the penalties for policyholders with claim sizes falling above and below the limit value. The number of claims is assumed to follow a Poisson distribution, and the total number of claims with a size greater than the limit value is considered a binomial distribution. The underlying risk of each policyholder is assumed to follow a beta Lindley distribution and is referred to as the prior distribution. Each policyholder’s claim size is also assumed to follow a gamma distribution, with the Lindley distribution considered as the prior distribution. Bonus-malus premiums are calculated following the Bayesian method. Practical examples using an actual data set are provided, and the results generated are compared to those produced using the traditional Poisson binomial-exponential beta model. This methodology provides a more equitable mechanism for penalizing policyholders in the portfolio.

Suggested Citation

  • Adisak Moumeesri & Tippatai Pongsart, 2022. "Bonus-Malus Premiums Based on Claim Frequency and the Size of Claims," Risks, MDPI, vol. 10(9), pages 1-22, September.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:9:p:181-:d:911309
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    References listed on IDEAS

    as
    1. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    2. Tzougas, George & Karlis, Dimitris & Frangos, Nicholas, 2017. "Confidence intervals of the premiums of optimal Bonus Malus Systems," LSE Research Online Documents on Economics 70926, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

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