Prudence and Higher-Order Risk Attitudes in the Rank-Dependent Utility Model

Abstract

We obtain a full characterization of consistency with respect to higher-order stochastic dominance within the rank-dependent utility model. Different from the results in the literature, we do not assume any conditions on the utility functions and the probability weighting function, such as differentiability or continuity. It turns out that the level of generality that we offer leads to models that do not have a continuous probability weighting function and yet they satisfy prudence. In particular, the corresponding probability weighting function can only have a jump at 1, and must be linear on [0, 1).

Keywords: Stochastic dominance, expected utility model, completely monotone functions, probability weighting, discontinuity