On the optimality of straight deductibles under smooth ambiguity aversion

Abstract

We solve the optimal insurance design problem under identifiable smooth ambiguity aversion with linear transaction cost. We impose monotonicity on indemnity schedules and their associated retention functions. Arrow’s cornerstone result that a straight deductible is optimal may fail to hold. We provide three conditions to restore it: (i) ambiguity does not affect large losses; (ii) priors are ordered according to first-order stochastic dominance and the probability of worse priors is greater conditional on observing a large loss than a small loss; or (iii) priors are ordered in the hazard rate order. We also derive comparative statics and find intuitive results.