IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v231y2026ics0167715225002743.html

Generalized reflected backward doubly SDEs with irregular barriers and continuous coefficients

Author

Listed:
  • Elmansouri, Badr
  • Marzougue, Mohamed

Abstract

In this note, we establish the existence of a minimal solution for a class of reflected generalized backward doubly stochastic differential equations with continuous and stochastic linear growth coefficients. The reflecting obstacle is not assumed to be right-continuous, but only right-upper semi-continuous and left-limited, and the noise is driven by two mutually independent Brownian motions and an independent integer-valued random measure. Our analysis begins with the case of stochastic Lipschitz coefficients, where we prove the existence and uniqueness results along with presenting a comparison result, which then allows us to derive the main existence finding of a minimal solution.

Suggested Citation

  • Elmansouri, Badr & Marzougue, Mohamed, 2026. "Generalized reflected backward doubly SDEs with irregular barriers and continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:stapro:v:231:y:2026:i:c:s0167715225002743
    DOI: 10.1016/j.spl.2025.110629
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715225002743
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2025.110629?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. Aman, Auguste & Mrhardy, Naoul, 2013. "Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 863-874.
    2. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    3. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2017. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Post-Print hal-01141801, HAL.
    4. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    5. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    6. Li, Zhi & Luo, Jiaowan, 2012. "One barrier reflected backward doubly stochastic differential equations with discontinuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1841-1848.
    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. Libo Li & Ruyi Liu & Marek Rutkowski, 2026. "Vulnerable European and American options in a hazard-process model," Finance and Stochastics, Springer, vol. 30(2), pages 553-596, April.
    2. Daniel Chee & Noufel Frikha & Libo Li, 2026. "A Monotone Limit Approach to Entropy-Regularized American Options," Papers 2602.18062, arXiv.org.
    3. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    4. Qian, Hongchao, 2025. "Mean reflected backward stochastic differential equations with jumps in a convex domain," Statistics & Probability Letters, Elsevier, vol. 223(C).
    5. Daniel Chee & Noufel Frikha & Libo Li, 2026. "Entropy-regularized penalization schemes and reflected BSDEs with singular generators," Papers 2602.18078, arXiv.org, revised Mar 2026.
    6. Marco Rodrigues, 2025. "Robust Hedging of American Options via Aggregated Snell Envelopes," Papers 2506.14553, arXiv.org.
    7. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    8. Ihsan Arharas & Siham Bouhadou & Youssef Ouknine, 2022. "Doubly Reflected Backward Stochastic Differential Equations in the Predictable Setting," Journal of Theoretical Probability, Springer, vol. 35(1), pages 115-141, March.
    9. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.
    10. Abdelkarim Oualaid & Khaled Bahlali & Youssef Ouknine, 2023. "Reflected Backward Stochastic Differential Equations Associated to Jump Markov Processes and Application to Partial Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1400-1436, September.
    11. Marzougue, Mohamed, 2020. "A note on optional Snell envelopes and reflected backward SDEs," Statistics & Probability Letters, Elsevier, vol. 165(C).
    12. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2021. "American options in a non-linear incomplete market model with default," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 479-512.
    13. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.
    14. Daniel Chee & Noufel Frikha & Libo Li, 2026. "Entropy-regularized penalization schemes for American options and reflected BSDEs with singular generators," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05520660, HAL.
    15. Hilbert, Astrid & Jarni, Imane & Ouknine, Youssef, 2020. "On reflected stochastic differential equations driven by regulated semimartingales," Statistics & Probability Letters, Elsevier, vol. 167(C).
    16. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "European options in a non-linear incomplete market model with default," Working Papers hal-02025833, HAL.
    17. Grigorova, Miryana & Imkeller, Peter & Ouknine, Youssef & Quenez, Marie-Claire, 2020. "Optimal stopping with f-expectations: The irregular case," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1258-1288.
    18. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2020. "European options in a non-linear incomplete market model with default," Post-Print hal-02025833, HAL.
    19. Qian, Hongchao, 2026. "Mean reflected backward stochastic partial differential equations," Statistics & Probability Letters, Elsevier, vol. 229(C).
    20. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2019. "Superhedging prices of European and American options in a non-linear incomplete market with default," Center for Mathematical Economics Working Papers 607, Center for Mathematical Economics, Bielefeld University.

    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:stapro:v:231:y:2026:i:c:s0167715225002743. 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.