Cash-invariant hull representation of divergence preferences

2026-07-03

AI Summary

This study addresses the complexity and limited applicability of existing characterizations of Uniformly Weighted Divergence Preferences (UWDP) by proposing a simpler, computationally tractable representation. By constructing a translation-invariant envelope of state-independent expected utility over the L⁰ space and leveraging tools from convex analysis, duality theory, and variational methods in spaces of probability measures, the paper establishes—for the first time under full generality—the equivalence between UWDP and this envelope. The resulting formulation not only unveils the intrinsic structure of UWDP but also substantially enhances its operationality and interpretability, yielding several important theoretical implications.

Abstract

Uniformly weighted divergence preferences (UWDP) introduced in Maccheroni et al. (2006) are an important class of risk-averse preferences that contain as a special case the monotone mean--variance utility. UWDP are characterised by the lowest expected value of an act in $L^\infty$ under an adversarially chosen probability measure combined with the divergence of this measure. Our main result provides an alternative, computationally friendlier formula, which establishes in full generality that UWDP are the translation-invariant hull of state-independent expected utility over $L^0$. Some consequences of the new representation are studied.

Problem

• divergence preferences
• uniformly weighted divergence preferences
• translation-invariant hull
• expected utility
• risk-averse preferences

Innovation

• uniformly weighted divergence preferences
• translation-invariant hull
• state-independent expected utility
• risk-averse preferences
• computational representation