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Tightness and duality of martingale transport on the Skorokhod space

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  • Guo, Gaoyue
  • Tan, Xiaolu
  • Touzi, Nizar

Abstract

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 càdlàg 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.

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  • Guo, Gaoyue & Tan, Xiaolu & Touzi, Nizar, 2017. "Tightness and duality of martingale transport on the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 927-956.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:3:p:927-956
    DOI: 10.1016/j.spa.2016.07.005
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    Cited by:

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    2. Bruno Bouchard & Xiaolu Tan, 2021. "A quasi-sure optional decomposition and super-hedging result on the Skorokhod space," Finance and Stochastics, Springer, vol. 25(3), pages 505-528, July.
    3. Ariel Neufeld, 2018. "Buy-And-Hold Property For Fully Incomplete Markets When Super-Replicating Markovian Claims," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-12, December.
    4. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    5. Forde, Martin, 2019. "Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European, One-Touch, lookback or forward starting options," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 799-821.
    6. Erhan Bayraktar & Shuoqing Deng & Dominykas Norgilas, 2023. "Supermartingale Brenier’s Theorem with Full-Marginal Constraint," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 17, pages 569-636, World Scientific Publishing Co. Pte. Ltd..
    7. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    8. Yan Dolinsky, 2023. "Delayed Semi-static Hedging in the Continuous Time Bachelier Model," Papers 2311.17270, arXiv.org, revised Dec 2023.
    9. Julien Claisse & Gaoyue Guo & Pierre Henry-Labordère, 2018. "Some Results on Skorokhod Embedding and Robust Hedging with Local Time," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 569-597, November.
    10. Matti Kiiski, 2020. "The Riesz representation theorem and weak∗ compactness of semimartingales," Finance and Stochastics, Springer, vol. 24(4), pages 827-870, October.
    11. Daniel Bartl & Michael Kupper & David J. Promel & Ludovic Tangpi, 2017. "Duality for pathwise superhedging in continuous time," Papers 1705.02933, arXiv.org, revised Apr 2019.
    12. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.
    13. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.

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