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A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets.
The general moment problem, a geometric approach
J. H. B. Kemperman · 1968
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Duality theorems for marginal problems
H.G. Kellerer · 1984
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Linear programming in infinite-dimensional spaces
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On Hoeffding-Fréchet bounds and cyclic monotone relations
M. Knott and C. Smith · 1992
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The geometry of optimal transportation
W. Gangbo and R. McCann · 1996
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On c c -optimal random variables
L. Rüschendorf · 1996
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A simple geometric proof that comonotonic risks have the convex-largest sum
R. Kaas, J. Dhaene, D. Vyncke, M.J. Goovaerts, and M. Denuit · 2002
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Existence and stability results in the L 1 L^{1} theory of optimal transportation
L. Ambrosio and A. Pratelli · 2003
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On a class of multidimensional optimal transportation problems
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Topics in optimal transportation
C. Villani · 2003
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The Skorokhod embedding problem and its offspring
J. Obłój · 2004
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On the sufficiency of c c -cyclical monotonicity for optimality of transport plans
A. Pratelli · 2008
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Optimal and better transport plans
M. Beiglböck, M. Goldstern, G. Maresch, and W. Schachermayer · 2009
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Characterization of optimal transport plans for the Monge-Kantorovich problem
W. Schachermayer and J. Teichmann · 2009
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Optimal Transport. Old and New
C. Villani · 2009
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On optimality of c c -cyclically monotone transference plans
S. Bianchini and L. Caravenna · 2010
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Moments, Positive Polynomials and Their Applications
Jean-Bernard Lasserre · 2010
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The Skorokhod embedding problem and model-independent bounds for option prices
D. Hobson · 2011
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Uniqueness and Monge solutions in the multimarginal optimal transportation problem
B. Pass · 2011
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Optimal transportation with infinitely many marginals
B. Pass · 2013
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Martingale optimal transport and robust hedging in continuous time
Y. Dolinsky and M. H. Soner · 2014
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Robust hedging with proportional transaction costs
Y. Dolinsky and M. H. Soner · 2014
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A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
A. Galichon, P. Henry-Labordère, and N. Touzi · 2014
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Arbitrage and duality in nondominated discrete-time models
B. Bouchard and M. Nutz · 2015
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On the Monge-Kantorovich problem with additional linear constraints
D. Zaev · 2015
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