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arXiv · 1902.05763

Weak monotone rearrangement on the line

Julio Backhoff-Veraguas·Mathias Beiglböck·Gudmund Pammer
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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.

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Julio Backhoff-Veraguas, Mathias Beiglböck, Gudmund Pammer. 2019-02-15. Weak monotone rearrangement on the line. https://arxiv.org/abs/1902.05763

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