Prudence and higher-order risk attitudes in the rank-dependent utility model

TL;DR

This paper characterizes when rank-dependent utility models are consistent with higher-order stochastic dominance without assuming smoothness, revealing models with discontinuous probability weighting functions that still satisfy prudence.

Contribution

It provides a comprehensive characterization of higher-order stochastic dominance consistency in rank-dependent utility models without smoothness assumptions, allowing for discontinuous probability weighting functions.

Findings

Models can have jump discontinuities at 1 in their probability weighting functions.

Such models can still satisfy prudence despite lack of continuity.

The characterization broadens understanding of rank-dependent utility models' flexibility.

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 condition on the utility functions and the probability weighting functions, 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).