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Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains

Author

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  • Arthur Charpentier

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Arthur David

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Romuald Elie

    (LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we investigate the impact of the claim 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. A numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed.

Suggested Citation

  • Arthur Charpentier & Arthur David & Romuald Elie, 2016. "Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains," Working Papers hal-01326798, HAL.
    • Handle: RePEc:hal:wpaper:hal-01326798
    Note: View the original document on HAL open archive server: https://hal.science/hal-01326798v1
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    References listed on IDEAS

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    1. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    2. 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.
    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. 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.
    5. 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.
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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. Aivars Spilbergs & Andris Fomins & Māris Krastiņš, 2022. "Multivariate Modelling of Motor Third Party Liability Insurance Claims," European Journal of Business Science and Technology, Mendel University in Brno, Faculty of Business and Economics, vol. 8(1), pages 5-18.

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    Keywords

    bonus malus; markov chains;

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