Weak monotone rearrangement on the line

Julio Backhoff-Veraguas; Mathias Beiglböck; Gudmund Pammer

doi:10.1214/20-ecp292

Weak monotone rearrangement on the line

Julio Backhoff-Veraguas, Mathias Beiglböck, Gudmund Pammer

Research output: Contribution to journal › Article › peer-review

Abstract

Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in mathematical finance.

In this note we provide a complete geometric characterization of the weak version of the classical monotone rearrangement between measures on the real line, complementing earlier results of Alfonsi, Corbetta, and Jourdain.

Original language	English
Pages (from-to)	1-16
Journal	Electronic Communications in Probability
Volume	25
DOIs	https://doi.org/10.1214/20-ecp292
Publication status	Published - 1 Jan 2020
Externally published	Yes

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10.1214/20-ecp292Licence: CC BY 4.0

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title = "Weak monotone rearrangement on the line",

abstract = "Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in mathematical finance.In this note we provide a complete geometric characterization of the weak version of the classical monotone rearrangement between measures on the real line, complementing earlier results of Alfonsi, Corbetta, and Jourdain.",

author = "Julio Backhoff-Veraguas and Mathias Beiglb{\"o}ck and Gudmund Pammer",

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AB - Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in mathematical finance.In this note we provide a complete geometric characterization of the weak version of the classical monotone rearrangement between measures on the real line, complementing earlier results of Alfonsi, Corbetta, and Jourdain.

U2 - 10.1214/20-ecp292

DO - 10.1214/20-ecp292

M3 - Article

SN - 1083-589X

VL - 25

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JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

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Weak monotone rearrangement on the line

Abstract

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