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Constrained Optimal Transport

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  • Ibrahim Ekren
  • H. Mete Soner

Abstract

The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\cal{X}$ with a order unit. The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of $\cal{X}$ and the dual problem is defined on the bi-dual of $\cal{X}$. These results are then applied to several extensions of the classical optimal transport.

Suggested Citation

  • Ibrahim Ekren & H. Mete Soner, 2016. "Constrained Optimal Transport," Papers 1610.02940, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1610.02940
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    File URL: http://arxiv.org/pdf/1610.02940
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    References listed on IDEAS

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    7. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
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    Cited by:

    1. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545, arXiv.org, revised Apr 2019.
    2. Stephan Eckstein & Michael Kupper, 2018. "Computation of optimal transport and related hedging problems via penalization and neural networks," Papers 1802.08539, arXiv.org, revised Jan 2019.

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