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Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains

Author

Listed:
  • Arthur Charpentier

    (Faculte des Sciences Economiques, Universite Rennes 1, 7 Place Hoche, 35065 Rennes CEDEX, France)

  • Arthur David

    (Faculte des Sciences Economiques, Universite Rennes 1, 7 Place Hoche, 35065 Rennes CEDEX, France)

  • Romuald Elie

    (Batiment Bois de l’Etang, Universite Paris Est, 5 rue Galilee, 77420 Champs sur Marne, France)

Abstract

In this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. Mathematical properties of the induced level class process are studied. A convergent numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:58-:d:118079
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Michael Braun & Peter S. Fader & Eric T. Bradlow & Howard Kunreuther, 2006. "Modeling the "Pseudodeductible" in Insurance Claims Decisions," Management Science, INFORMS, vol. 52(8), pages 1258-1272, August.
    4. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    5. Christoph Haehling von Lanzenauer, 1974. "Optimal Claim Decisions by Policyholders in Automobile Insurance with Merit-Rating Structures," Operations Research, INFORMS, vol. 22(5), pages 979-990, October.
    6. De Pril, Nelson, 1979. "Optimal Claim Decisions for a Bonus-Malus System: a Continuous Approach," ASTIN Bulletin, Cambridge University Press, vol. 10(2), pages 215-222, March.
    7. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    8. Lemaire, Jean & Zi, Hongmin, 1994. "A Comparative Analysis of 30 Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 287-309, November.
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    Cited by:

    1. Martinek, László & Arató, N. Miklós, 2019. "An approach to merit rating by means of autoregressive sequences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 205-217.
    2. Arthur Charpentier & Lariosse Kouakou & Matthias Lowe & Philipp Ratz & Franck Vermet, 2021. "Collaborative Insurance Sustainability and Network Structure," Papers 2107.02764, arXiv.org, revised Sep 2022.
    3. Darren Shannon & Tim Jannusch & Florian David‐Spickermann & Martin Mullins & Martin Cunneen & Finbarr Murphy, 2021. "Connected and autonomous vehicle injury loss events: Potential risk and actuarial considerations for primary insurers," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 24(1), pages 5-35, March.

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