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Tightness and duality of martingale transport on the Skorokhod space

Guo, Gaoyue; Tan, Xiaolu; Touzi, Nizar (2017), Tightness and duality of martingale transport on the Skorokhod space, Stochastic Processes and their Applications, 127, 3, p. 927-956. 10.1016/j.spa.2016.07.005

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Stochastic Processes and their Applications
Volume
127
Number
3
Publisher
Elsevier
Pages
927-956
Publication identifier
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Author(s)
Guo, Gaoyue
Tan, Xiaolu
Touzi, Nizar
Abstract (EN)
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 .
Subjects / Keywords
S−topology; dynamic programming principle; robust superhedging