Optimal insurance design of ambiguous risks

Abstract

We examine the characteristics of the optimal insurance contract under linear transaction costs and an ambiguous distribution of losses. Under the standard expected utility model, we know from Arrow (1965) that it contains a straight deductible. In this paper, we assume that the policyholder is ambiguity averse in the sense of Klibanoff et al. (Econometrica 73(6):1849–1892, 2005). The optimal contract depends upon the structure of the ambiguity. For example, if the set of possible priors can be ranked according to the monotone likelihood ratio order, the optimal contract contains a disappearing deductible. We also show that the policyholder’s ambiguity aversion may have the counterintuitive effect to reduce the optimal insurance coverage of an ambiguous risk.