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Martingale transport plans on the line are known from Beiglbock & Juillet to have an irreducible decomposition on a (at most) countable union of intervals.
The existence of probability measures with given marginals
Volker Strassen · 1965
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Measurable relations
Charles J Himmelberg · 1975
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Survey of measurable selection theorems
Daniel H Wagner · 1977
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Stochastic optimal control: The discrete time case
Dimitri P Bertsekas and Steven E Shreve · 1978
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Duality theorems for marginal problems
Hans G Kellerer · 1984
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Contribution à l’étude de la mesurabilité, de la loi de probabilité et de la convergence des multifonctions
Christian Hess · 1986
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A polish topology for the closed subsets of a polish space
Gerald Beer · 1991
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A general version of the fundamental theorem of asset pricing
Freddy Delbaen and Walter Schachermayer · 1994
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Robust pricing and hedging of double no-touch options
Alexander MG Cox and Jan Obłój · 2011
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The skorokhod embedding problem and model-independent bounds for option prices
David Hobson · 2011
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Robust bounds for forward start options
David Hobson and Anthony Neuberger · 2012
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Model-independent bounds for option prices: a mass transport approach
Mathias Beiglböck, Pierre Henry-Labordère, and Friedrich Penkner · 2013
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Convex analysis and minimization algorithms I: Fundamentals
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 2013
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A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
Alfred Galichon, Pierre Henry-Labordere, and Nizar Touzi · 2014
Structure of optimal martingale transport plans in general dimensions
Nassif Ghoussoub, Young-Heon Kim, and Tongseok Lim · 2015
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Robust price bounds for the forward starting straddle
David Hobson and Martin Klimmek · 2015
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Convex analysis
Ralph Tyrell Rockafellar · 2015
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On the monge–kantorovich problem with additional linear constraints
Danila A Zaev · 2015
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On a problem of optimal transport under marginal martingale constraints
Mathias Beiglböck and Nicolas Juillet · 2016
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Cited alongside, same era.
Complete duality for martingale optimal transport on the line
Mathias Beiglböck, Marcel Nutz, and Nizar Touzi · 2015
Cited alongside, same era.
Ibrahim Ekren and H Mete Soner · 2016
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Structure of martingale transports in finite dimensions
Jan Oblój and Pietro Siorpaes · 2017
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