  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.
