Open Access
November 2019 A Benamou–Brenier formulation of martingale optimal transport
Martin Huesmann, Dario Trevisan
Bernoulli 25(4A): 2729-2757 (November 2019). DOI: 10.3150/18-BEJ1069


We introduce a Benamou–Brenier formulation for the continuous-time martingale optimal transport problem as a weak length relaxation of its discrete-time counterpart. By the correspondence between classical martingale problems and Fokker–Planck equations, we obtain an equivalent PDE formulation for which basic properties such as existence, duality and geodesic equations can be analytically studied, yielding corresponding results for the stochastic formulation. In the one dimensional case, sufficient conditions for finiteness of the cost are also given and a link between geodesics and porous medium equations is partially investigated.


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Martin Huesmann. Dario Trevisan. "A Benamou–Brenier formulation of martingale optimal transport." Bernoulli 25 (4A) 2729 - 2757, November 2019.


Received: 1 September 2017; Revised: 1 June 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110110
MathSciNet: MR4003563
Digital Object Identifier: 10.3150/18-BEJ1069

Keywords: Fokker–Planck equations , Martingale optimal transport , Martingale problem , porous medium equation , Strassen’s theorem

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4A • November 2019
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