Ambiguity on the Insurer's Side: The Demand for Insurance
46 Pages Posted: 30 Jan 2015 Last revised: 18 Jun 2015
Date Written: January 27, 2015
Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., Hogarth and Kunreuther (1989)). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then optimal indemnity schedules exist and are monotonic. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., Huberman, Mayers, and Smith (1983)). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow on the optimality of the deductible indemnity schedule.
Keywords: Optimal Insurance, Deductible, Ambiguity, Choquet Integral, Distorted Probabilities
JEL Classification: G22
Suggested Citation: Suggested Citation