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Optimal insurance with adverse selection and comonotonic background risk

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  • David Alary

    (LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

  • Franck Bien

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this note, we consider an adverse selection problem involving an insurance market à la Rothschild-Stiglitz. We assume that part of the loss is uninsurable as in the case with health care or environmental risk. We characterize sufficient conditions such that adverse selection by itself does not distort competitive insurance contracts. A sufficiently large uninsurable loss provides an incentive to high-risk policy holders not to mimic low-risk policy holders without distorting the optimal coverage.

Suggested Citation

  • David Alary & Franck Bien, 2019. "Optimal insurance with adverse selection and comonotonic background risk," Working Papers hal-02390017, HAL.
    • Handle: RePEc:hal:wpaper:hal-02390017
    Note: View the original document on HAL open archive server: https://hal.science/hal-02390017
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    References listed on IDEAS

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    1. Doherty, Neil A & Schlesinger, Harris, 1983. "The Optimal Deductible for an Insurance Policy When Initial Wealth Is Random," The Journal of Business, University of Chicago Press, vol. 56(4), pages 555-565, October.
    2. Neil A. Doherty & Harris Schlesinger, 1990. "Rational Insurance Purchasing: Consideration of Contract Nonperformance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 243-253.
    3. Neil A. Doherty & Hong Joo Jung, 1993. "Adverse Selection When Loss Severities Differ: First-Best and Costly Equilibria," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 18(2), pages 173-182, December.
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    Keywords

    Adverse Selection; Background risk; Optimal Contract;
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