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Robust expected utility maximization with medial limits

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  • Daniel Bartl
  • Patrick Cheridito
  • Michael Kupper

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.

Suggested Citation

  • Daniel Bartl & Patrick Cheridito & Michael Kupper, 2017. "Robust expected utility maximization with medial limits," Papers 1712.07699, arXiv.org, revised Nov 2018.
    • Handle: RePEc:arx:papers:1712.07699
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    File URL: http://arxiv.org/pdf/1712.07699
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    References listed on IDEAS

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    1. Laurence Carassus & Romain Blanchard, 2016. "Robust Optimal Investment in Discrete Time for Unbounded Utility Function," Papers 1609.09205, arXiv.org, revised Oct 2017.
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    7. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
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    Cited by:

    1. Huy N. Chau & Miklos Rasonyi, 2018. "Robust utility maximization in markets with transaction costs," Papers 1803.04213, arXiv.org, revised Dec 2018.

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