Preference robust distortion risk measures

2026-08-03

AI Summary

This study addresses the ambiguity inherent in the risk functional itself—distinct from distributional uncertainty—within risk preference models. It pioneers the integration of robust optimization into the space of distortion functions by constructing ambiguity sets based on Wasserstein distance and Bregman divergence, and derives closed-form solutions for distortion risk measures under worst- and best-case scenarios. The framework is further extended to rank-dependent utility models, revealing them as robust counterparts of expected utility under ambiguity in the risk functional. This insight offers a novel explanation for the Allais paradox and yields a preference-robust decision model capable of capturing and interpreting behavioral biases.

Abstract

We introduce a framework for preference-robust decision making when preferences over risk are modelled through generalised distortion risk measures. Unlike distributional robustness, our approach addresses ambiguity in the risk functional itself. We construct ambiguity sets on distortion (weight) functions using the Wasserstein distance and Bregman divergences, and derive closed-form expressions for the worst- and best-case distortion risk measures. We further extend the framework to rank-dependent utility, yielding preference-robust behavioural models. In particular, rank-dependent utility appears as a robustification of the expected utility model, yielding a novel way to address the Allais paradox.

Problem

• preference robustness
• distortion risk measures
• risk functional ambiguity
• rank-dependent utility
• Allais paradox

Innovation

• preference robustness
• distortion risk measures
• Wasserstein distance
• Bregman divergence
• rank-dependent utility