The Optimality of a Safe Choice in the Rank-Dependent Utility Model

Abstract

We study the optimality of a safe choice in the rank-dependent utility model. We first show in a general decision problem that a safe choice is not optimal if this choice is not the highest choice, and the first order risk aversion measure of an agent's utility function at the payoff from the safe choice is strictly smaller than the gain-loss ratio of the marginal payoff from the safe choice under the transformed probability distribution, or this choice is not the lowest choice, and the first order risk aversion measure is strictly smaller than the reciprocal of that gain-loss ratio; if the condition is reversed then the safe choice is optimal under pseudoconcavity. We then apply the result to four classic decision problems, namely a two-asset portfolio problem, a coinsurance problem, a deductible insurance problem, and a hedging problem, and present a necessary and sufficient condition for the optimality of a riskless portfolio, full coinsurance, full deductible insurance, and a fully hedged position, respectively.