1. Tightness and duality of martingale transport on the Skorokhod space
- Author
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Nizar Touzi, Gaoyue Guo, Xiaolu Tan, The Institute of Automation of the Chinese Academy of Sciences (CASIA), Chinese Academy of Sciences [Beijing] (CAS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Statistics and Probability ,01 natural sciences ,FOS: Economics and business ,010104 statistics & probability ,Mathematics::Probability ,0502 economics and business ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,robust superhedging ,Mathematics - Optimization and Control ,Mathematics ,Probability measure ,050208 finance ,Applied Mathematics ,Mathematical finance ,Probability (math.PR) ,05 social sciences ,dynamic programming principle ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Dynamic programming ,Optimization and Control (math.OC) ,S−topology ,Modeling and Simulation ,Pricing of Securities (q-fin.PR) ,Martingale (probability theory) ,Quantitative Finance - Pricing of Securities ,Mathematics - Probability - Abstract
International audience; The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of c`adì ag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S−topology and the dynamic programming principle 1 .
- Published
- 2017