IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v187y2025ics0304414925001048.html
   My bibliography  Save this article

Lp-solutions of multi-dimensional BSDEs with mean reflection

Author

Listed:
  • Niu, Yue
  • Qu, Baoyou
  • Wang, Falei

Abstract

The present paper focuses on the investigation of multi-dimensional mean reflected backward stochastic differential equations (BSDEs) in a possibly non-convex reflection domain, whose generator also depends on the marginal probability distributions of the solution (Y,Z). Our main idea is to decompose the mean reflected BSDE into a BSDE and a deterministic Skorokhod problem. Then, utilizing Lp-estimates for BSDEs and Skorokhod problems, we explore the solvability of Lp-solutions (p>1) through fixed-point argument and an approximation approach under both inward normal and oblique reflection scenarios.

Suggested Citation

  • Niu, Yue & Qu, Baoyou & Wang, Falei, 2025. "Lp-solutions of multi-dimensional BSDEs with mean reflection," Stochastic Processes and their Applications, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:spapps:v:187:y:2025:i:c:s0304414925001048
    DOI: 10.1016/j.spa.2025.104663
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001048
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104663?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. Rainer Buckdahn & Ying Hu, 1998. "Pricing of American Contingent Claims with Jump Stock Price and Constrained Portfolios," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 177-203, February.
    2. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    3. Ying Hu & Remi Moreau & Falei Wang, 2024. "General Mean Reflected Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(1), pages 877-904, March.
    4. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    5. Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
    6. Briand, Philippe & Hibon, Hélène, 2021. "Particles Systems for mean reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 253-275.
    7. Klimsiak, Tomasz & Rozkosz, Andrzej & Słomiński, Leszek, 2015. "Reflected BSDEs in time-dependent convex regions," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 571-596.
    8. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    9. Bénézet, Cyril & Chassagneux, Jean-François & Richou, Adrien, 2022. "Switching problems with controlled randomisation and associated obliquely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 23-71.
    10. Philippe Briand & Romuald Elie & Ying Hu, 2018. "BSDEs with mean reflection," Post-Print hal-01318649, HAL.
    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. Qian, Hongchao, 2025. "Mean reflected backward stochastic differential equations with jumps in a convex domain," Statistics & Probability Letters, Elsevier, vol. 223(C).
    2. Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(C).
    3. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. Li, Hanwu, 2024. "Backward stochastic differential equations with double mean reflections," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    5. Aazizi, Soufiane & El Mellali, Tarik & Fakhouri, Imade & Ouknine, Youssef, 2018. "Optimal switching problem and related system of BSDEs with left-Lipschitz coefficients and mixed reflections," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 70-78.
    6. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    7. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    8. Klimsiak, Tomasz, 2019. "Systems of quasi-variational inequalities related to the switching problem," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1259-1286.
    9. He, Wei, 2024. "Multi-dimensional mean-reflected BSDEs driven by G-Brownian motion with time-varying non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 206(C).
    10. Luo, Peng & Zhu, Mengbo, 2024. "Diagonally quadratic BSDE with oblique reflection and optimal switching," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    11. Ying Hu & Remi Moreau & Falei Wang, 2024. "General Mean Reflected Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(1), pages 877-904, March.
    12. Chassagneux, Jean-François & Richou, Adrien, 2019. "Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4597-4637.
    13. Djehiche, Boualem & Dumitrescu, Roxana & Zeng, Jia, 2025. "A propagation of chaos result for weakly interacting nonlinear Snell envelopes," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    14. An, Jongbong & Jeon, Junkee & Kim, Takwon, 2025. "Optimal portfolio and retirement decisions with costly job switching options," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    15. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    16. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    17. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    18. Dumitrescu, Roxana & Elie, Romuald & Sabbagh, Wissal & Zhou, Chao, 2023. "A new Mertens decomposition of Yg,ξ-submartingale systems. Application to BSDEs with weak constraints at stopping times," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 183-205.
    19. Perninge, Magnus, 2024. "Optimal stopping of BSDEs with constrained jumps and related zero-sum games," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    20. Graewe, Paulwin & Popier, Alexandre, 2021. "Asymptotic approach for backward stochastic differential equation with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 247-277.

    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:187:y:2025:i:c:s0304414925001048. 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.