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The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice.
Optimal martingale transport between radially symmetric marginals in general dimensions
T. Lim · 1912
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On the transfer of masses
L. V. Kantorovich · 1942
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On a problem of Monge
L. V. Kantorovich · 1948
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The existence of probability measures with given marginals
V. Strassen · 1965
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Characterization of the subdifferentials of convex functions
R.T. Rockafellar · 1966
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Prices of state-contingent claims implicit in option prices
D.T. Breeden and R.H. Litzenberger · 1978
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Duality theorems for marginal problems
H. Kellerer · 1984
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Construction of multivariate distributions with marginals Given
L. Rüschendorf · 1985
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Polar factorization and monotone rearrangement of vector-valued functions
Y. Brenier · 1991
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The geometry of optimal transportation
W. Gangbo and R.J. McCann · 1996
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Partial differential equations and Monge-Kantorovich mass transfer
L.C. Evans · 1997
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A convexity principle for interacting gases
R. J. McCann · 1997
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Robust hedging of the lookback option
D. Hobson · 1998
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A Riemannian interpolation inequality á la Borell, Brascamp and Lieb
D. Cordero-Erausquin, R. J. McCann, and M. Schmuckenschläger · 2001
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Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
L.A. Caffarelli, M. Feldman, and R. J. McCann · 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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Topics in optimal transportation
C. Villani · 2003
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Existence of optimal transport maps for crystalline norms
L. Ambrosio, B. Kirchheim, and A. Pratelli · 2004
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The Skorokhod embedding problem and its offspring
J. Obłój · 2004
Cited alongside, same era.
Regularity of potential functions of the optimal transportation problem
X. N. Ma, N. S. Trudinger, and X. J. Wang · 2005
Cited alongside, same era.
Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
D. Cordero-Erausquin, R. J. McCann, and M. Schmuckenschläger · 2006
Cited alongside, same era.
On strict convexity and continuous differentiability of potential functions in optimal transportation
N. S. Trudinger and X. J. Wang · 2009
Cited alongside, same era.
Optimal Transport. Old and New
C. Villani · 2009
Cited alongside, same era.
The Monge problem for strictly convex norms in ℝ d {\mathbb{R}}^{d}
T. Champion and L. De Pascale · 2010
Cited alongside, same era.
Robust price bounds for the forward starting straddle
D. Hobson and M. Klimmek · 2014
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Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
F. Santambrogio · 2015
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On the Monge-Kantorovich problem with additional linear constraints
D. Zaev · 2015
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On a problem of optimal transport under marginal martingale constraints
M. Beiglböck and N. Juillet · 2016
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Vector quantile regression: an optimal transport approach
G. Carlier, V. Chernozhukov and A. Galichon · 2016
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On the monotonicity principle of optimal Skorokhod embedding problem
G. Guo, X. Tan and N. Touzi · 2016
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Quantile and Probability Curves without Crossing
V. Chernozhukov, I. Fernandez-Val and A. Galichon · 2010
Cited alongside, same era.
The Monge problem in ℝ d {\mathbb{R}}^{d}
T. Champion and L. De Pascale · 2011
Cited alongside, same era.
When is multidimensional screening a convex program?
A. Figalli,Y-H Kim and R.J. McCann · 2011
Cited alongside, same era.
The Skorokhod embedding problem and model-independent bounds for option prices
D. Hobson · 2011
Cited alongside, same era.
On Azéma-Yor processes, their optimal properties and the Bachelier-drawdown equation
L. Carraro, N.E. Karoui and J. Obłój · 2012
Cited alongside, same era.
Robust bounds for forward start options
D. Hobson and A. Neuberger · 2012
Cited alongside, same era.
Closest in time.
Optimal Skorokhod embedding under finitely-many marginal constraints
G. Guo, X. Tan and N. Touzi · 2016
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Optimal transport and Skorokhod embedding
M. Beiglböck, A.M.G. Cox, and M. Huesmann · 2017
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Complete duality for martingale optimal transport on the line
M. Beiglböck, M. Nutz and N. Touzi · 2017
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Monge-Kantorovich depth, quantiles, ranks and signs
V. Chernozhukov, A. Galichon, M. Hallin, and M. Henry · 2017
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An iterated Azéma-Yor type embedding for finitely many marginals
J. Obłój and P. Spoida · 2017
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Dual attainment for the martingale transport problem
M. Beiglböck, T. Lim and J. Obłój · 2019
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The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach
A.M.G. Cox, J. Obłój and N. Touzi · 2019
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Irreducible convex paving for decomposition of multidimensional martingale transport plans
H. De March and N. Touzi · 2019
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Structure of optimal martingale transport plans in general dimensions
N. Ghoussoub, Y-H. Kim, and T. Lim · 2019
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Optimal Brownian stopping when the source and target are radially symmetric distributions
N. Ghoussoub, Y-H. Kim, and T. Lim · 2020
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Identification of hedonic equilibrium and nonseperable simultaneous equations
V. Chernozhukov, A. Galichon, M. Henry, and B. Pass · 2021
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Robust Pricing and Hedging of Options on Multiple Assets and Its Numerics
S. Eckstein, G. Guo, T. Lim, and J. Obłój · 2021
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