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M. Beiglböck:
"Shadow couplings and related extremal peacocks";
Talk: Workshop on Stochastic Analysis and Mathematical Finance, Oaxaca, Mexiko (invited); 2016-05-23; in: "Stochastic Analysis and Mathematical Finance - A Fruitful Partnership", (2016), 3.

A classical result of Strassen asserts that given probabilities on the real line which are in convex order, there exists a martingale coupling with these marginals. Remarkably, it is a non trivial problem to construct particular solutions to this problem. In this article, we introduce a family of such martingale couplings,
each of which admits several characterizations in terms of optimality properties / geometry of the support set / representation through a Skorokhod embedding. As one particular element of this family we recover the (left) monotone martingale transport which can be viewed as a martingale analogue of the classical monotone
rearrangement. As another canonical element of this family we identify a martingale coupling that resembles the usual product coupling and enjoys several curious properties related Lipschitz-kernels and general transport costs as recently introduced by Gozlan etal. Finally we shall consider the multi-period martingales
/ peacocks related to these couplings. (joint work with Nicolas Juillet)

http://www.birs.ca/events/2016/5-day-workshops/16w5134/schedule