Abstract

This paper investigates the impact of an ambiguity increase on the optimal insurance deductible for a risk- and ambiguity-averse individual under the uncertainty of a loss distribution. A deductible is an important insurance contract design in both theory and practice. Previous studies have reported preference-based results in the context of coinsurance, albeit with limited applications. In this paper, we prove a straight deductible is optimal under an α-maxmin model. In the context of the straight deductible, we assume that the cumulative loss probability at an initial optimal deductible is preserved after an ambiguity increase. We show that, for a loss below the initial optimal deductible, the optimal deductible remains unchanged when possible distributions are unaffected by the ambiguity increase. Allowing for a distinct center in the belief set while keeping the others unchanged, we prove that, when the worst distribution is unaffected, but the best distribution deteriorates in terms of first-order stochastic dominance, the optimal deductible becomes lower after the ambiguity increase. If the cumulative loss probability is not preserved, the optimal deductible decreases when, at the initial optimal deductible, the odds of obtaining partial indemnity relative to no indemnity become larger under the loss distribution distorted by ambiguity aversion.  

Keywords

ambiguity increaseambiguity aversionoptimal insurance coveragedeductibleα-maxmin model