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arXiv · 1804.04283

Transport plans with domain constraints

Erhan Bayraktar·Xin Zhang·Zhou Zhou
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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.

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Erhan Bayraktar, Xin Zhang, Zhou Zhou. 2018-04-12. Transport plans with domain constraints. https://arxiv.org/abs/1804.04283

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