Weak monotone rearrangement on the line

Julio Backhoff-Veraguas; Mathias Beiglboeck; Gudmund Pammer

doi:10.1214/20-ECP292

Weak monotone rearrangement on the line

Julio Backhoff-Veraguas, Mathias Beiglboeck, Gudmund Pammer

Mathematics of Operations Research

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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
Article number	18
Number of pages	16
Journal	Electronic Communications in Probability
Volume	25
DOIs	https://doi.org/10.1214/20-ECP292
Publication status	Published - 2020

Keywords

Convex order
Martingale transport
Mass transport
Monotone rearrangement

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10.1214/20-ECP292Licence: CC BY

20-ECP292Final published version, 709 KBLicence: CC BY

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Weak monotone rearrangement on the line

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Keywords

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