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April 2017 Optimal Skorokhod embedding given full marginals and Azéma–Yor peacocks
Sigrid Källblad, Xiaolu Tan, Nizar Touzi
Ann. Appl. Probab. 27(2): 686-719 (April 2017). DOI: 10.1214/16-AAP1191


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.


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Sigrid Källblad. Xiaolu Tan. Nizar Touzi. "Optimal Skorokhod embedding given full marginals and Azéma–Yor peacocks." Ann. Appl. Probab. 27 (2) 686 - 719, April 2017.


Received: 1 March 2015; Revised: 1 October 2015; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60075
MathSciNet: MR3655851
Digital Object Identifier: 10.1214/16-AAP1191

Primary: 60G40 , 91G80
Secondary: 60G44 , 91J20

Keywords: martingale inequality , martingale transport problem , maximum of martingale given marginals , peacocks , Skorokhod embedding problem

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 2 • April 2017
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