Publications in Scientific Journals:

M. Beiglböck, M. Nutz, N. Touzi:
"Complete Duality for Martingale Optimal Transport on the Line";
Annals of Probability, June (2016), 1 - 42.

English abstract:
We study the optimal transport between two probability measures
on the real line, where the transport plans are laws of one-step mar-
tingales. 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 ageneralprincipleofcyclicalmonotonicitydescribingthegeometryof
optimal transports.

Martingale Optimal Transport Kantorovich Duality AMS 2010 Subject Classification 60G42; 49N05

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.