Publications in Scientific Journals:
S. Källblad, X. Tan, N. Touzi:
"Optimal Skorokhod embedding given full marginals and Azéma-Yor peacocks";
Annals of Applied Probability,
Volume 27 (First available in Project Euclid: 26 May 2017)
We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0,1]. The problem is related to the study of extremal martingales associated with a peacock ("process increasing in convex order," by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the martingale transport problem studied in Henry-Labordère, Obłój, Spoida and Touzi [Ann. Appl. Probab. 26 (2016) 1-44]. Under technical conditions, we then characterize the optimal value and the solution to the dual problem. In particular, the optimal embedding corresponds to the Madan and Yor [Bernoulli 8 (2002) 509-536] peacock under their "increasing mean residual value" condition. We also discuss the associated martingale inequality.
Mathematical Reviews number (MathSciNet): MR3655851
Skorokhod embedding problem peacocks martingale inequality martingale transport problem maximum of martingale given marginals
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