Beiglböck, M., Nutz, M., & Touzi, N. (2016). Complete Duality for Martingale Optimal Transport on the Line. Annals of Probability, 45(5), 3038–3074. https://doi.org/10.1214/16-aop1131
Statistics and Probability; Statistics, Probability and Uncertainty; 49N05; Martingale Optimal Transport Kantorovich Duality AMS 2010 Subject Classification 60G42
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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.
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Research Areas:
Mathematical Methods in Economics: 50% Fundamental Mathematics Research: 50%
