Talks and Poster Presentations (with Proceedings-Entry):
"Martingale Benamou-Brenier: a probabilistic perspective";
Talk: 13th German Probability and Statistics Days 2018,
Universität Freiburg, Germany (invited);
2018-02-27; in: "GPSD - 13th German Probability and Statistics Days - Freiburger Stochastik-Tage, February 27-March 2, 2018",
In classical optimal transport, the contributions by Benamou, Brenier and McCann (among others)regarding the time-dependent version of the problem, have had a lasting impact in the field and ledto many applications. It is remarkable that this is achieved even if in continuous time classical optimaltransport, mass/particles only travel in straight lines. Of course this fails to happen when we consider(continuous-time) martingale optimal transport; namely when we only allow for martingale couplingsin the transport problem.In this talk we discuss the existence of a martingale analogue to McCann´s interpolation and theBenamou-Brenier formula from a probabilistic - as opposed to analytic - point of view. This remarkablemartingale is characterized by very natural optimality and geometric properties: in a precise way, itprovides a canonical martingale way to connect two measures in convex order.
Joint work with: Mathias Beiglböck, Martin Huesmann, Sigrid Källbla
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.