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Budget-constrained optimal insurance without the nonnegativity constraint on indemnities

Mario Ghossoub

Insurance: Mathematics and Economics, 2019, vol. 84, issue C, 22-39

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.

Keywords: Optimal insurance; Deductible contract; Nonnegativity constraint; Ambiguity; Knightian uncertainty; Non-additive probability; Probability distortion; Choquet integral (search for similar items in EconPapers)
JEL-codes: C02 D86 G22 (search for similar items in EconPapers)
Date: 2019
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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