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M. Beiglböck:
"A Benamou-Brenier type problem for martingale transport";
Talk: CIRM Luminy, Marseille, Frankreich (invited); 2017-11-13 - 2017-11-17.

: In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas. We suggest a Benamou-Brenier type formulation of the martingale transport problem for given d-dimensional distributions µ, ν in convex order. The unique solution M of this problem turns out to be a Markov-martingale
which has several notable properties: In a specific sense, it mimics the movement of a Brownian particle as closely as possible subject to the conditions M0 ∼ µ, M1 ∼ ν. Similar to McCann´s displacementinterpolation, it provides a time-consistent interpolation between µ and ν. For particular choices of the initial and terminal law, it recovers archetypical martingales such as
Brownian motion, geometric Brownian motion, and the Bass martingale. Furthermore, it yields a natural approximation to the local vol model and a new approach to Kellerer´s theorem.
(Joint work with J. Backhoff, M. Huesmann and S. Kallblad)

https://conferences.cirm-math.fr/1730.html