Complete duality for martingale optimal transport on the line

Mathias Beiglböck, Marcel Nutz, Nizar Touzi
2017 Annals of Probability  
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
more » ... a general principle of cyclical monotonicity describing the geometry of optimal transports.
doi:10.1214/16-aop1131 fatcat:sjrvlolj2jct5o5i5dsdum5fe4