An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint

Abstract

We provide an extension of the martingale version of the Frechet–Hoeffding coupling to the infinitely-many marginals constraints setting. In the two-marginal context, this extension was obtained by Beiglbock and Juillet (2016), and further developed by Henry-Labordere and Touzi (in press), see also Beiglbock and Henry-Labordere (Preprint).