Publications in Scientific Journals:
M. Beiglböck, M. Nutz, N. Touzi:
"Complete duality for martingale optimal transport on the line";
Annals of Probability,
Volume 45
(2017),
Issue 5;
3038
- 3074.
English abstract:
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to fail in the classical formulation. As a consequence of the duality result, we obtain a general principle of cyclical monotonicity describing the geometry of optimal transports.
Keywords:
Martingale optimal transport Kantorovich duality
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1214/16-AOP1131
Electronic version of the publication:
http://publik.tuwien.ac.at/files/publik_266685.pdf
Created from the Publication Database of the Vienna University of Technology.