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Refundable deductible insurance

Author

Listed:
  • Maria Mercè Claramunt

    (UB - Universitat de Barcelona)

  • Maite Màrmol

Abstract

Most insurance policies include a deductible, so that a part of the claim is assumed by the insured. In order to get a full coverage of the claim, the insured has two options: hire a Zero Deductible Insurance or take out an insurance policy with deductible and, simultaneously, a Refundable Deductible Insurance. The objective of this paper is to analyze these two options, comparing the premium paid. We define dif (F) as the difference between the premiums paid. This function depends on the parameters of the deductible applied, and we focus our attention on the sign of this difference and the calculation of the optimal deductible, that is, the values of the parameters of the deductible that allows us to obtain the greatest reduction in the global premium.

Suggested Citation

  • Maria Mercè Claramunt & Maite Màrmol, 2020. "Refundable deductible insurance," Working Papers hal-02909299, HAL.
    • Handle: RePEc:hal:wpaper:hal-02909299
    Note: View the original document on HAL open archive server: https://hal.science/hal-02909299
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    References listed on IDEAS

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    1. Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, December.
    3. Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
    4. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605, October.
    5. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    6. Hua, Lei & Cheung, Ka Chun, 2008. "Worst allocations of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 93-98, August.
    7. Robert L. Winkler & Gary M. Roodman & Robert R. Britney, 1972. "The Determination of Partial Moments," Management Science, INFORMS, vol. 19(3), pages 290-296, November.
    8. Lemaire, Jean & Zi, Hongmin, 1994. "High Deductibles instead of Bonus-Malus: Can it Work?," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 75-86, May.
    9. 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.
    10. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    11. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    12. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    13. Mark J. Machina, 1995. "Non-Expected Utility and The Robustness of the Classical Insurance Paradigm," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 9-50, June.
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    Keywords

    premium calculation; variance criterion; optimization;
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