Cash-invariant hull representation of divergence preferences

Summary · qwen2.5:32b

The article presents a new, computationally more efficient formula for representing uniformly weighted divergence preferences (UWDP), showing they are the translation-invariant hull of state-independent expected utility over $L^0$. This reformulation is significant as it simplifies the computation and analysis of risk-averse preferences that include monotone mean-variance utility. The key detail is the use of a cash-invariant hull representation to characterize UWDP under an adversarially chosen probability measure combined with divergence.

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Excerpt

arXiv:2607.03305v1 Announce Type: cross 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.