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Bonus–Malus systems with Weibull distributed claim severities

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  • Ni, Weihong
  • Constantinescu, Corina
  • Pantelous, Athanasios A.

Abstract

One of the pricing strategies for Bonus–Malus (BM) systems relies on the decomposition of the claims’ randomness into one part accounting for claims’ frequency and the other part for claims’ severity. By mixing an exponential with a Lévy distribution, we focus on modelling the claim severity component as a Weibull distribution. For a Negative Binomial number of claims, we employ the Bayesian approach to derive the BM premiums for Weibull severities. We then conclude by comparing our explicit formulas and numerical results with those for Pareto severities that were introduced by Frangos & Vrontos.

Suggested Citation

  • Ni, Weihong & Constantinescu, Corina & Pantelous, Athanasios A., 2014. "Bonus–Malus systems with Weibull distributed claim severities," Annals of Actuarial Science, Cambridge University Press, vol. 8(2), pages 217-233, September.
    • Handle: RePEc:cup:anacsi:v:8:y:2014:i:02:p:217-233_00
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    Cited by:

    1. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    2. Cheung, Eric C.K. & Ni, Weihong & Oh, Rosy & Woo, Jae-Kyung, 2021. "Bayesian credibility under a bivariate prior on the frequency and the severity of claims," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 274-295.
    3. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    4. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    5. Li, Bo & Ni, Weihong & Constantinescu, Corina, 2015. "Risk models with premiums adjusted to claims number," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 94-102.

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