Tightness and duality of martingale transport on the Skorokhod space *

Gaoyue Guo (1) , Xiaolu Tan (2) , Nizar Touzi (3)

1 CASIA - The Institute of Automation of the Chinese Academy of Sciences
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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 .

Mots clés: S−topology; dynamic programming principle; robust superhedging

Domaines: Probabilités [math.PR]

Gaoyue Guo, Xiaolu Tan, Nizar Touzi. Tightness and duality of martingale transport on the Skorokhod space *. Stochastic Processes and their Applications, 2017. ⟨hal-01247005⟩