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An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint

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  • Henry-Labordère, Pierre
  • Tan, Xiaolu
  • Touzi, Nizar

Abstract

We provide an extension of the martingale version of the Fréchet–Hoeffding coupling to the infinitely-many marginals constraints setting. In the two-marginal context, this extension was obtained by Beiglböck and Juillet (2016), and further developed by Henry-Labordère and Touzi (in press), see also Beiglböck and Henry-Labordère (Preprint).

Suggested Citation

  • Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2800-2834
    DOI: 10.1016/j.spa.2016.03.003
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    Cited by:

    1. Nicole Bäuerle & Daniel Schmithals, 2019. "Martingale optimal transport in the discrete case via simple linear programming techniques," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 453-476, December.
    2. Nutz, Marcel & Stebegg, Florian & Tan, Xiaowei, 2020. "Multiperiod martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1568-1615.
    3. Aur'elien Alfonsi & Jacopo Corbetta & Benjamin Jourdain, 2017. "Sampling of probability measures in the convex order by Wasserstein projection," Papers 1709.05287, arXiv.org, revised Feb 2019.
    4. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    5. Mathias Beiglböck & Gudmund Pammer & Walter Schachermayer, 2022. "From Bachelier to Dupire via optimal transport," Finance and Stochastics, Springer, vol. 26(1), pages 59-84, January.
    6. Beiglböck, Mathias & Henry-Labordère, Pierre & Touzi, Nizar, 2017. "Monotone martingale transport plans and Skorokhod embedding," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3005-3013.
    7. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.
    8. Mathias Beiglboeck & Pierre Henry-Labordere & Nizar Touzi, 2017. "Monotone Martingale Transport Plans and Skorohod Embedding," Papers 1701.06779, arXiv.org.
    9. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.
    10. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    11. Benjamin Jourdain & Gilles Pagès, 2022. "Convex Order, Quantization and Monotone Approximations of ARCH Models," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2480-2517, December.
    12. Nicole Bauerle & Daniel Schmithals, 2019. "Consistent upper price bounds for exotic options given a finite number of call prices and their convergence," Papers 1907.09144, arXiv.org.

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