Weak monotone rearrangement on the line

2019/02/15 by Backhoff-Veraguas, Julio, Beiglböck, Mathias, Pammer, Gudmund · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1902.05763

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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