Robust expected utility maximization with medial limits

TL;DR

This paper develops a robust expected utility maximization framework in discrete time that handles nondominated model uncertainty using medial limits, providing existence conditions and dual representations without assuming time-consistency.

Contribution

It introduces a novel approach employing medial limits and a general representation for monotone convex functionals to address model uncertainty without time-consistency assumptions.

Findings

Optimal strategies exist under specified conditions.

Dual representations for the utility are derived.

Applicable to problems with moment and Wasserstein constraints.

Abstract

In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach is based on a general representation result for monotone convex functionals, a functional version of Choquet's capacitability theorem and medial limits. The novelty is that it works under nondominated model uncertainty without any assumptions of time-consistency. As applications, we discuss robust utility maximization problems with moment constraints, Wasserstein constraints and Wasserstein penalties.