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A classical result of Strassen asserts that given probabilities $\mu, \nu$ on the real line which are in convex order, there exists a \emph{martingale coupling} with these marginals, i.e.\ a random vector $(X_1,X_2)$ such that $X_1\sim \mu, X_2\sim \nu$ and $E[X_2|X_1]=X_1$.
The existence of probability measures with given marginals
V. Strassen · 1965
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Characterization of the subdifferentials of convex functions
R. Rockafellar · 1966
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Stopping times on Brownian motion: Some properties of Root’s construction
R. M. Loynes · 1970
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Markov-Komposition und eine Anwendung auf Martingale
H. Kellerer · 1972
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On embedding right continuous martingales in Brownian motion
I. Monroe · 1972
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Integraldarstellung von Dilationen
H. G. Kellerer · 1973
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Fitting Martingales To Given Marginals
G. Lowther · 2008
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Optimal transport
C. Villani · 2009
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Peacocks and associated martingales, with explicit constructions
F. Hirsch, C. Profeta, B. Roynette, and M. Yor · 2011
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A new proof of Kellerer’s theorem
F. Hirsch and B. Roynette · 2012
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Robust bounds for forward start options
D. Hobson and A. Neuberger · 2012
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Model-independent bounds for option prices: A mass transport approach
M. Beiglböck, P. Henry-Labordère, and F. Penkner · 2013
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Robust price bounds for the forward starting straddle
D. Hobson and M. Klimmek · 2013
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An optimality principle with applications in optimal transport
M. Beiglböck and C. Griessler · 2014
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Change of numeraire in the two-marginals martingale transport problem
L. Campi, I. Laachir, and C. Martini · 2014
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Martingale optimal transport and robust hedging in continuous time
Y. Dolinsky and H. M. Soner · 2014
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Monotone Martingale Transport Plans and Skorokhod Embedding
M. Beiglböck, P. Henry-Labordère, and N. Touzi · 2015
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Complete Duality for Martingale Optimal Transport on the Line
M. Beiglböck, M. Nutz, and N. Touzi · 2015
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Arbitrage and duality in nondominated discrete-time models
B. Bouchard and M. Nutz · 2015
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Optimal transport and skorokhod embedding
M. Beiglböck, A. Cox, and M. Huesmann · 2016
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Root to Kellerer
M. Beiglböck, M. Huesmann, and F. Stebegg · 2016
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On a problem of optimal transport under marginal martingale constraints
M. Beiglböck and N. Juillet · 2016
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