Regret-based optimal insurance design
In this paper, we investigate an optimal insurance design problem in which the insured's risk preference is of the regret-theoretical expected utility type and admissible insurance contracts are set to satisfy both the principle of indemnity and the incentive-compatible condition. When the insurance premium is calculated by the expected value principle, we show that the optimal solution for a regret-averse insured can be in the form of no insurance or partial insurance above a deductible. We obtain a necessary and sufficient condition for the optimality of no insurance and provide a numerical algorithm to derive the optimal partial insurance above a deductible. Notably, the deductible disappears if and only if the insurance premium is actuarially fair. Finally, we carry out a comparative statics analysis to examine the effect of the insured's regret coefficient on the insured's final wealth and insurance demand.
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