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Is a Refundable Deductible Insurance an advantage for the insured? a mathematical approach

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  • M Mercè Claramunt
  • Maite Mármol

Abstract

Most insurance policies include a deductible, so that a part of the claim is paid by the insured. In order to get full coverage of the claim, the insured has two options: purchase a Zero Deductible Insurance Policy or purchase an insurance policy with deductible together with Refundable Deductible Insurance. The objective of this paper is to analyze these two options and compare the premium paid by each. We define dif(P) 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 allow us to obtain the greatest reduction in the premium.

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  • M Mercè Claramunt & Maite Mármol, 2021. "Is a Refundable Deductible Insurance an advantage for the insured? a mathematical approach," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-22, February.
    • Handle: RePEc:plo:pone00:0247030
    DOI: 10.1371/journal.pone.0247030
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    References listed on IDEAS

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    1. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363.
    2. Pitrebois, Sandra & Walhin, Jean-François & Denuit, Michel, 2005. "Bonus-malus Systems with Varying Deductibles," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 261-274, May.
    3. 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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    1. Claramunt, M. Mercè & Costa, Teresa & Mármol, Maite & Varea, Xavier, 2024. "Household Refundable Utility by taking out refundable insurance: Empirical study in the Spanish auto insurance market," Economics Letters, Elsevier, vol. 241(C).

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