Revisiting Optimal Insurance Design Under Smooth Ambiguity Aversion

Abstract

We analyze optimal insurance design for a risk- and ambiguity-averse policyholder who is uncertain about the distribution of losses and faces linear transaction costs. We use smooth ambiguity preferences, a flexible ambiguity structure, and focus on indemnity schedules that satisfy the principle of indemnity and the no-sabotage condition for incentive compatibility. We characterize optimal insurance contracts and find that the marginal indemnity is either zero or one except at critical points. We then provide a condition for a straight deductible to be optimal and show that this condition is satisfied under various stochastic ordering assumptions on the priors. We discuss specific ambiguity structures, some of which give rise to indemnities with multiple layers. We also derive comparative statics. Greater ambiguity aversion always raises insurance demand whereas greater ambiguity has indeterminate effects. For policyholders with relative ambiguity prudence between zero and two, greater ambiguity raises insurance demand.

Keywords: insurance design, risk sharing, ambiguity, deductible, no-sabotage condition, comparative statics

JEL Classification: D81, D86, G22