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The True Claim Amount and Frequency Distributions within a Bonus-Malus System

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  • Walhin, Jean François
  • Paris, José

Abstract

We apply Lemaire's algorithm and a non-parametric mixed Poisson fit to a motor insurance portfolio in order to find the true claim frequency and claim amount distributions. The algorithm we develop accounts for the fact that observed distributions are distorted by bonus hunger, when a bonus-malus system is used by the insurer.

Suggested Citation

  • Walhin, Jean François & Paris, José, 2000. "The True Claim Amount and Frequency Distributions within a Bonus-Malus System," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 391-403, November.
    • Handle: RePEc:cup:astinb:v:30:y:2000:i:02:p:391-403_01
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    Cited by:

    1. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
    2. Arthur Charpentier & Arthur David & Romuald Elie, 2017. "Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains," Risks, MDPI, vol. 5(4), pages 1-17, November.
    3. Chu-Shiu Li & Chwen-Chi Liu & Sheng-Chang Peng, 2013. "Expiration Dates in Automobile Insurance Contracts: The Curious Case of Last Policy Month Claims in Taiwan," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 38(1), pages 23-47, March.
    4. Jean‐Philippe Boucher & Michel Denuit & Montserrat Guillen, 2009. "Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 821-846, December.
    5. Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.

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