OPTIMAL SKOROKHOD EMBEDDING GIVEN FULL MARGINALS AND AZEMA-YOR PEACOCKS

• 成果类型: Article
• 署名作者: Kaellblad, Sigrid; Tan, Xiaolu; Touzi, Nizar
• 署名单位: Technische Universitat Wien; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1191
• 发表日期: 2017
• 页码: 686-719
• 关键词: maximum maximum; martingale

摘要

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-Labordere, Obloj, 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.