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We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales.
The existence of probability measures with given marginals
V. Strassen · 1965
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Stochastic Optimal Control. The Discrete-Time Case
D. P. Bertsekas and S. E. Shreve · 1978
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Duality theorems for marginal problems
H. G. Kellerer · 1984
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A general version of the fundamental theorem of asset pricing
F. Delbaen and W. Schachermayer · 1994
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Robust hedging of the lookback option
D. Hobson · 1998
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C. Villani · 2003
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The Skorokhod embedding problem and its offspring
J. Obłój · 2004
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Measure theory. Vol. I
V. I. Bogachev · 2007
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Optimal and better transport plans
M. Beiglböck, M. Goldstern, G. Maresch, and W. Schachermayer · 2009
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Optimal transport, old and new
C. Villani · 2009
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A. M. G. Cox and J. Obłój · 2011
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The Skorokhod embedding problem and model-independent bounds for option prices
D. Hobson · 2011
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L. Ambrosio and N. Gigli · 2013
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Model-independent bounds for option prices: a mass transport approach
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An explicit martingale version of Brenier’s theorem
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