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S. Källblad:
"Optimal Skorokhod embedding given full marginals and application to the maximal reward function";
Talk: Workshop "Optimal transport and stochastics", Hausdorff Center for Mathematics, University Bonn, Germany (invited); 2018-03-09.

We consider here the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0,1]. The problem is related to studying the extremal martingales associated to a peacock ("process increasing in convex ordering", by Hirsch, Profeta, Roynette and Yor (2011)). A general duality result is obtained by convergence techniques. We then study the case where the reward functions depends on the maximum of the embedding process, which is the limit of the martingale transport problem studied in Henry-Labordere, Obloj, Spoida and Touzi (2014). Under technical conditions, some explicit characteristics of the solutions to the optimal SEP as well as to its dual problem are obtained. We also discuss the associated martingale inequality. This is joint work with Xiaolu Tan and Nizar Touzi.

https://www.him.uni-bonn.de/en/programs/past-programs/past-junior-trimester-programs/optimal-transportation/workshop-optimal-transport-and-stochastics/schedule/#c7187