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A Benamou-Brenier formulation of martingale optimal transport

Authors :
Huesmann, Martin
Trevisan, Dario
Publication Year :
2017

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.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1707.01493
Document Type :
Working Paper