preprint

Inserted: 8 jan 2018

Year: 2017

Abstract:

We identify a Benamou--Brenier formulation for the continuous-time martingale optimal transport problem obtained as a weak length relaxation of its discrete-time counterpart. Using the general correspondence between classical martingale problem 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. Sufficient conditions for finiteness of the cost are also given, and, in the one dimensional case, a link between geodesics and porous medium equations is partially investigated.