IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v176y2021ics0167715221000936.html
   My bibliography  Save this article

On the stability of the martingale optimal transport problem: A set-valued map approach

Author

Listed:
  • Neufeld, Ariel
  • Sester, Julian

Abstract

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglböck et al. (2021), we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals.

Suggested Citation

  • Neufeld, Ariel & Sester, Julian, 2021. "On the stability of the martingale optimal transport problem: A set-valued map approach," Statistics & Probability Letters, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000936
    DOI: 10.1016/j.spl.2021.109131
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221000936
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109131?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mathias Beiglboeck & Pierre Henry-Labordere & Nizar Touzi, 2017. "Monotone Martingale Transport Plans and Skorohod Embedding," Papers 1701.06779, arXiv.org.
    2. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.
    3. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    4. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
    5. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    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 Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    8. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandro Doldi & Marco Frittelli, 2023. "Entropy martingale optimal transport and nonlinear pricing–hedging duality," Finance and Stochastics, Springer, vol. 27(2), pages 255-304, April.
    2. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    3. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
    4. Ariel Neufeld & Julian Sester, 2021. "A deep learning approach to data-driven model-free pricing and to martingale optimal transport," Papers 2103.11435, arXiv.org, revised Dec 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.
    2. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    3. Ariel Neufeld & Julian Sester, 2021. "On the stability of the martingale optimal transport problem: A set-valued map approach," Papers 2102.02718, arXiv.org, revised Apr 2021.
    4. Nutz, Marcel & Stebegg, Florian & Tan, Xiaowei, 2020. "Multiperiod martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1568-1615.
    5. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    6. 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.
    7. 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..
    8. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    9. Huesmann, Martin & Stebegg, Florian, 2018. "Monotonicity preserving transformations of MOT and SEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1114-1134.
    10. Aur'elien Alfonsi & Rafael Coyaud & Virginie Ehrlacher & Damiano Lombardi, 2019. "Approximation of Optimal Transport problems with marginal moments constraints," Papers 1905.05663, arXiv.org.
    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. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545, arXiv.org, revised Apr 2019.
    13. Lim, Tongseok, 2020. "Optimal martingale transport between radially symmetric marginals in general dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1897-1912.
    14. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867, arXiv.org, revised Nov 2017.
    15. Luciano Campi & Ismail Laachir & Claude Martini, 2017. "Change of numeraire in the two-marginals martingale transport problem," Finance and Stochastics, Springer, vol. 21(2), pages 471-486, April.
    16. Zhengqing Zhou & Jose Blanchet & Peter W. Glynn, 2021. "Distributionally Robust Martingale Optimal Transport," Papers 2106.07191, arXiv.org, revised Nov 2021.
    17. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.
    18. Marcel Nutz & Florian Stebegg & Xiaowei Tan, 2017. "Multiperiod Martingale Transport," Papers 1703.10588, arXiv.org, revised May 2019.
    19. Linn Engstrom & Sigrid Kallblad & Johan Karlsson, 2024. "Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport," Papers 2406.09959, arXiv.org.
    20. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000936. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.