IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01326798.html
   My bibliography  Save this paper

Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains

Author

Listed:
  • 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-01326798
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01326798/document
    Download Restriction: no
    ---><---

    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Dhiti Osatakul & Xueyuan Wu, 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment," Risks, MDPI, vol. 9(1), pages 1-23, January.
    3. Guillermo Gallego & Ruxian Wang & Ming Hu & Julie Ward & Jose Luis Beltran, 2015. "No Claim? Your Gain: Design of Residual Value Extended Warranties Under Risk Aversion and Strategic Claim Behavior," Manufacturing & Service Operations Management, INFORMS, vol. 17(1), pages 87-100, February.
    4. 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.
    5. Søren Asmussen, 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction," Risks, MDPI, vol. 2(1), pages 1-25, March.
    6. Xiaodong Du & Hongli Feng & David A. Hennessy, 2017. "Rationality of Choices in Subsidized Crop Insurance Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 99(3), pages 732-756.
    7. 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.
    8. Xiaodong Du & Hongli Feng & David A. Hennessy, 2017. "Rationality of Choices in Subsidized Crop Insurance Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 99(3), pages 732-756.
    9. Ming-Jyh Wang & Chieh-Hua Wen & Lawrence W Lan, 2010. "Modelling Different Types of Bundled Automobile Insurance Choice Behaviour: The Case of Taiwan*," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 35(2), pages 290-308, April.
    10. Gaganis, Chrysovalantis & Hasan, Iftekhar & Pasiouras, Fotios, 2016. "Regulations, institutions and income smoothing by managing technical reserves: International evidence from the insurance industry," Omega, Elsevier, vol. 59(PA), pages 113-129.
    11. Hurlimann, W., 1998. "On distribution-free safe layer-additive pricing," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 277-285, July.
    12. David H. Krantz & Howard C. Kunreuther, 2007. "Goals and plans in decision making," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 2, pages 137-168, June.
    13. Michael Braun & André Bonfrer, 2011. "Scalable Inference of Customer Similarities from Interactions Data Using Dirichlet Processes," Marketing Science, INFORMS, vol. 30(3), pages 513-531, 05-06.
    14. Voleti, Sudhir & Srinivasan, V. & Ghosh, Pulak, 2017. "An approach to improve the predictive power of choice-based conjoint analysis," International Journal of Research in Marketing, Elsevier, vol. 34(2), pages 325-335.
    15. Asma Teimouri & Mahbanoo Tata & Mohsen Rezapour & Rafal Kulik & Narayanaswamy Balakrishnan, 2021. "Asymptotic Behavior of Eigenvalues of Variance-Covariance Matrix of a High-Dimensional Heavy-Tailed Lévy Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1353-1375, December.
    16. 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.
    17. 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.
    18. Benjamin L. Collier & Daniel Schwartz & Howard C. Kunreuther & Erwann O. Michel-Kerjan, 2017. "Risk Preferences in Small and Large Stakes: Evidence from Insurance Contract Decisions," NBER Working Papers 23579, National Bureau of Economic Research, Inc.
    19. Sudhir Voleti & Pulak Ghosh, 2013. "A robust approach to measure latent, time-varying equity in hierarchical branding structures," Quantitative Marketing and Economics (QME), Springer, vol. 11(3), pages 289-319, September.
    20. repec:cup:judgdm:v:2:y:2007:i::p:137-168 is not listed on IDEAS
    21. Marius Dan Gavriletea & Aura Carmen Moga, 2011. "Romanian Compulsory Motor Third Party Liability Insurance In 2010 And The Predictable Future," Annales Universitatis Apulensis Series Oeconomica, Faculty of Sciences, "1 Decembrie 1918" University, Alba Iulia, vol. 1(13), pages 1-9.

    More about this item

    Keywords

    bonus malus; markov chains;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-01326798. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.