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arXiv · 1712.07699

Robust expected utility maximization with medial limits

Daniel Bartl·Patrick Cheridito·Michael Kupper
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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.

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Daniel Bartl, Patrick Cheridito, Michael Kupper. 2017-12-20. Robust expected utility maximization with medial limits. https://doi.org/10.1016/j.jmaa.2018.11.012

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