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.
Citation
Julio Backhoff-Veraguas. Mathias Beiglböck. Gudmund Pammer. "Weak monotone rearrangement on the line." Electron. Commun. Probab. 25 1 - 16, 2020. https://doi.org/10.1214/20-ECP292
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