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September 2017 Complete duality for martingale optimal transport on the line
Mathias Beiglböck, Marcel Nutz, Nizar Touzi
Ann. Probab. 45(5): 3038-3074 (September 2017). DOI: 10.1214/16-AOP1131


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.


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Mathias Beiglböck. Marcel Nutz. Nizar Touzi. "Complete duality for martingale optimal transport on the line." Ann. Probab. 45 (5) 3038 - 3074, September 2017.


Received: 1 July 2015; Revised: 1 May 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812200
MathSciNet: MR3706738
Digital Object Identifier: 10.1214/16-AOP1131

Primary: 49N05 , 60G42

Keywords: Kantorovich duality , Martingale optimal transport

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 5 • September 2017
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