Bernoulli

  • 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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1568362041

Digital Object Identifier
doi:10.3150/18-BEJ1069

Mathematical Reviews number (MathSciNet)
MR4003563

Zentralblatt MATH identifier
07110110

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

Citation

Huesmann, Martin; Trevisan, Dario. A Benamou–Brenier formulation of martingale optimal transport. Bernoulli 25 (2019), no. 4A, 2729--2757. doi:10.3150/18-BEJ1069. https://projecteuclid.org/euclid.bj/1568362041


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