The demand for insurance with ambiguous recovery rate

Abstract

It is not uncommon for insurance contracts to fail performing as intended. In practice, the default recovery rate is rather difficult to be evaluated precisely by insureds at the inception of the insurance contract. Thus, in this paper we assume ambiguous recovery rates and study optimal insurance demand for an insured. Under the insured’s identifiable smooth ambiguity preference, we derive conditions for the optimality of full insurance, partial insurance, or no insurance. In particular, we find that the introduction of ambiguity on the recovery rate raises the trigger level for full insurance to be optimal under actuarially fair contract pricing. We further carry out comparative statics to analyze the effect of the change in the degree of the insured’s ambiguity aversion or ambiguity level on the insurance demand. The insurance demand is reduced for a higher degree of ambiguity aversion or greater ambiguity, if certain conditions are imposed on the insurance pricing and the insured’s risk preference and ambiguity preference. We also examine the impact of the insured’s initial wealth, and find that the ambiguity reinforces the wealth effect when her coefficient of relative risk aversion is less than one.