A Benamou Brenier approach to martingale optimal transport

  • Martin Huesmann (Universität Bonn)
A3 01 (Sophus-Lie room)


We introduce and analyze a continuous time martingale optimal transport problem (MOT) which can be seen as the "Benamou-Brenier" formulation of MOT. It is naturally linked to the discrete MOT problem via a weak length relaxation. We present two different solutions to this problem. The first solution is based on a convex duality result and allows to derive a "geodesic equation" for the optimizer for a wide class of cost functions. The second is an explicit probabilistic representation in the case of a specific cost function. We will show that this solution has several applications as well as a remarkable additional optimality property.

(based on joint work with Julio Backhoff, Mathias Beiglböck, Sigrid Källblad, and Dario Trevisan)

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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