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 of the optimal utility. Our approach is based on medial limits , a functional version of Choquet's capacitability theorem and a general representation result for monotone convex functionals . The novelty is that it works in cases where robustness is described by a general family of probability measures that do not have to be dominated or time-consistent .
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 .
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a general representation result for monotone convex functionals
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in cases where robustness is described by a general family of probability measures that do not have to be dominated or time-consistent
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