• Bernoulli
  • Volume 25, Number 4A (2019), 2729-2757.

A Benamou–Brenier formulation of martingale optimal transport

Martin Huesmann and Dario Trevisan

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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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Bernoulli, Volume 25, Number 4A (2019), 2729-2757.

Received: September 2017
Revised: June 2018
First available in Project Euclid: 13 September 2019

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Fokker–Planck equations Martingale Optimal Transport martingale problem porous medium equation Strassen’s theorem


Huesmann, Martin; Trevisan, Dario. A Benamou–Brenier formulation of martingale optimal transport. Bernoulli 25 (2019), no. 4A, 2729--2757. doi:10.3150/18-BEJ1069.

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