Budget-constrained optimal insurance without the nonnegativity constraint on indemnities

The final publication is available at Elsevier via https://doi.org/10.1016/j.insmatheco.2018.10.004 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/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.Natural Sciences and Engineering Research Council [grant 2018-03961