IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v189y2025ics0304414925001309.html

Adapted Wasserstein distance between the laws of SDEs

Author

Listed:
  • Backhoff-Veraguas, Julio
  • Källblad, Sigrid
  • Robinson, Benjamin A.

Abstract

We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe–Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings.

Suggested Citation

  • Backhoff-Veraguas, Julio & Källblad, Sigrid & Robinson, Benjamin A., 2025. "Adapted Wasserstein distance between the laws of SDEs," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001309
    DOI: 10.1016/j.spa.2025.104689
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001309
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104689?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Veraguas, Julio Backhoff & Beiglböck, Mathias & Eder, Manu & Pichler, Alois, 2020. "Fundamental properties of process distances," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5575-5591.
    2. Iosif Il’ich Gihman & Anatoliĭ Vladimirovich Skorohod, 1979. "Controlled Stochastic Processes," Springer Books, Springer, number 978-1-4612-6202-2, January.
    3. 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.
    4. Iosif Il’ich Gihman & Anatoliĭ Vladimirovich Skorohod, 1979. "Discrete-Parameter Controlled Stochastic Processes," Springer Books, in: Controlled Stochastic Processes, chapter 1, pages 1-78, Springer.
    5. Liu, Yating & Pagès, Gilles, 2022. "Monotone convex order for the McKean–Vlasov processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 312-338.
    6. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    7. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
    8. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    9. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," LSE Research Online Documents on Economics 101864, London School of Economics and Political Science, LSE Library.
    10. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2918-2953.
    Full references (including those not matched with items on IDEAS)

    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. Beatrice Acciaio & Berenice Anne Neumann, 2025. "Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria," Mathematics and Financial Economics, Springer, volume 19, number 3, December.
    2. Julio Backhoff-Veraguas & Xin Zhang, 2023. "Dynamic Cournot-Nash equilibrium: the non-potential case," Mathematics and Financial Economics, Springer, volume 17, number 1, December.
    3. Bingyan Han, 2022. "Distributionally robust risk evaluation with a causality constraint and structural information," Papers 2203.10571, arXiv.org, revised Jun 2025.
    4. Mathias Beiglbock & Gudmund Pammer & Lorenz Riess, 2024. "Change of numeraire for weak martingale transport," Papers 2406.07523, arXiv.org.
    5. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    6. Ruslan Mirmominov & Johannes Wiesel, 2024. "A dynamic programming principle for multiperiod control problems with bicausal constraints," Papers 2410.23927, arXiv.org.
    7. Daniel Krv{s}ek & Gudmund Pammer, 2024. "General duality and dual attainment for adapted transport," Papers 2401.11958, arXiv.org, revised Nov 2024.
    8. Beatrice Acciaio & Daniel Krv{s}ek & Gudmund Pammer, 2024. "Multicausal transport: barycenters and dynamic matching," Papers 2401.12748, arXiv.org, revised Jan 2025.
    9. Daniel Bartl & Johannes Wiesel, 2022. "Sensitivity of multiperiod optimization problems in adapted Wasserstein distance," Papers 2208.05656, arXiv.org, revised Jun 2023.
    10. Beatrice Acciaio & Julio Backhoff-Veraguas & Junchao Jia, 2020. "Cournot-Nash equilibrium and optimal transport in a dynamic setting," Papers 2002.08786, arXiv.org, revised Nov 2020.
    11. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    12. Kupper, Michael & Nendel, Max & Sgarabottolo, Alessandro, 2025. "Risk measures based on weak optimal transport," Center for Mathematical Economics Working Papers 734, Center for Mathematical Economics, Bielefeld University.
    13. John Armstrong & Andrei Ionescu, 2023. "Gamma Hedging and Rough Paths," Papers 2309.05054, arXiv.org, revised Mar 2024.
    14. Gabriele Visentin & Patrick Cheridito, 2025. "Robust Optimization in Causal Models and G-Causal Normalizing Flows," Papers 2510.15458, arXiv.org.
    15. Cohen, Asaf & Saha, Subhamay, 2021. "Asymptotic optimality of the generalized cμ rule under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 206-236.
    16. Beatrice Acciaio & Stephan Eckstein & Songyan Hou, 2024. "Time-Causal VAE: Robust Financial Time Series Generator," Papers 2411.02947, arXiv.org.
    17. Nicolas Boursin & Carl Remlinger & Joseph Mikael & Carol Anne Hargreaves, 2022. "Deep Generators on Commodity Markets; application to Deep Hedging," Papers 2205.13942, arXiv.org.
    18. Beatrice Acciaio & Julio Backhoff & Gudmund Pammer, 2022. "Quantitative Fundamental Theorem of Asset Pricing," Papers 2209.15037, arXiv.org, revised Jan 2024.
    19. Michael Kupper & Max Nendel & Alessandro Sgarabottolo, 2023. "Risk measures based on weak optimal transport," Papers 2312.05973, arXiv.org.
    20. Benjamin Jourdain & Gudmund Pammer, 2023. "An extension of martingale transport and stability in robust finance," Papers 2304.09551, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spapps:v:189:y:2025:i:c:s0304414925001309. 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/505572/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.