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December 2019 Computational methods for martingale optimal transport problems
Gaoyue Guo, Jan Obłój
Ann. Appl. Probab. 29(6): 3311-3347 (December 2019). DOI: 10.1214/19-AAP1481

Abstract

We develop computational methods for solving the martingale optimal transport (MOT) problem—a version of the classical optimal transport with an additional martingale constraint on the transport’s dynamics. We prove that a general, multi-step multi-dimensional, MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretization of the marginal distributions combined with an appropriate relaxation of the martingale condition. Further, we establish two generic approaches for discretising probability distributions, suitable respectively for the cases when we can compute integrals against these distributions or when we can sample from them. These render our main result applicable and lead to an implementable numerical scheme for solving MOT problems. Finally, specialising to the one-step model on real line, we provide an estimate of the convergence rate which, to the best of our knowledge, is the first of its kind in the literature.

Citation

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Gaoyue Guo. Jan Obłój. "Computational methods for martingale optimal transport problems." Ann. Appl. Probab. 29 (6) 3311 - 3347, December 2019. https://doi.org/10.1214/19-AAP1481

Information

Received: 1 December 2018; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172336
MathSciNet: MR4047982
Digital Object Identifier: 10.1214/19-AAP1481

Subjects:
Primary: 49M25, 60H99
Secondary: 90C08

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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