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Budget-constrained optimal insurance without the nonnegativity constraint on indemnities

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  • Ghossoub, Mario

Abstract

In a problem of Pareto-efficient insurance contracting (bilateral risk sharing) with expected-utility preferences, Gollier (1987) relaxes the nonnegativity constraint on indemnities and argues that the existence of a deductible is only due to the variability in the cost of insurance, not the nonnegativity constraint itself. In this paper, we find support for a similar statement in problems of budget-constrained optimal insurance (i.e., demand for insurance). Specifically, we consider a setting of ambiguity (unilateral and bilateral) and a setting of belief heterogeneity. We drop the nonnegativity constraint and assume no cost (or a fixed cost) to the insurer, and we derive closed-form solutions to the problems that we formulate. In particular, we show that optimal indemnities no longer include a deductible provision; and they can be negative for small values of the loss, or in case of no loss.

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  • Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    • Handle: RePEc:eee:insuma:v:84:y:2019:i:c:p:22-39
    DOI: 10.1016/j.insmatheco.2018.10.004
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    4. Asimit, Alexandru V. & Cheung, Ka Chun & Chong, Wing Fung & Hu, Junlei, 2020. "Pareto-optimal insurance contracts with premium budget and minimum charge constraints," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 17-27.
    5. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    6. Sun, Huan & Wang, Haiyan & Steffensen, Sonja, 2022. "Mechanism design of multi-strategy health insurance plans under asymmetric information," Omega, Elsevier, vol. 107(C).
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    8. Boonen, Tim J. & Ghossoub, Mario, 2021. "Optimal reinsurance with multiple reinsurers: Distortion risk measures, distortion premium principles, and heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 23-37.
    9. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.

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    More about this item

    Keywords

    Optimal insurance; Deductible contract; Nonnegativity constraint; Ambiguity; Knightian uncertainty; Non-additive probability; Probability distortion; Choquet integral;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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