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Transport plans with domain constraints

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Listed:
  • Erhan Bayraktar
  • Xin Zhang
  • Zhou Zhou

Abstract

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.

Suggested Citation

  • Erhan Bayraktar & Xin Zhang & Zhou Zhou, 2018. "Transport plans with domain constraints," Papers 1804.04283, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1804.04283
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    References listed on IDEAS

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    1. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    2. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
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