IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v193y2023ics0167715222002310.html
   My bibliography  Save this article

Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients

Author

Listed:
  • Cui, Fengfeng
  • Zhao, Weidong

Abstract

This paper aims at solving a new type of BSDE with mean reflection under weaker assumptions on the coefficients. We establish the well-posedness of mean reflected BSDEs whenever the generator is non-Lipschitz in the y argument.

Suggested Citation

  • Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002310
    DOI: 10.1016/j.spl.2022.109718
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109718?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. 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. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    5. 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.
    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. Wang, Ying & Huang, Zhen, 2009. "Backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1438-1443, June.
    8. Fan, ShengJun & Jiang, Long, 2010. "Finite and infinite time interval BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 962-968, June.
    9. Hao, Tao & Wen, Jiaqiang & Xiong, Jie, 2022. "Solvability of a class of mean-field BSDEs with quadratic growth," Statistics & Probability Letters, Elsevier, vol. 191(C).
    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. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Fan, ShengJun & Jiang, Long, 2010. "Finite and infinite time interval BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 962-968, June.
    4. 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.
    5. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    6. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    7. Liu, Jicheng & Ren, Jiagang, 2002. "Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 93-100, January.
    8. Wu, Hao & Wang, Wenyuan & Ren, Jie, 2012. "Anticipated backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 672-682.
    9. Yu, Xianye, 2019. "Non-Lipschitz anticipated backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    10. Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
    11. Sheng-Jun Fan & Long Jiang, 2012. "A Generalized Comparison Theorem for BSDEs and Its Applications," Journal of Theoretical Probability, Springer, vol. 25(1), pages 50-61, March.
    12. Tie Wang & Siyu Cui, 2022. "Anticipated Backward Doubly Stochastic Differential Equations with Non-Lipschitz Coefficients," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    13. Wang, Ying & Huang, Zhen, 2009. "Backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1438-1443, June.
    14. Cody B. Hyndman & Polynice Oyono Ngou, 2017. "A Convolution Method for Numerical Solution of Backward Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 1-29, March.
    15. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    16. Fan, Shengjun & Hu, Ying & Tang, Shanjian, 2023. "Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 335-375.
    17. Xiong, Yafang & Xu, Xiaoming, 2020. "Anticipated backward stochastic differential equations with left-Lipschitz coefficient," Statistics & Probability Letters, Elsevier, vol. 163(C).
    18. Qin, Yan & Xia, Ning-Mao, 2013. "Variational approach for the adapted solution of the general backward stochastic differential equations under the Bihari condition," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1271-1281.
    19. Fan, ShengJun & Liu, DeQun, 2010. "A class of BSDE with integrable parameters," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2024-2031, December.
    20. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.

    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:193:y:2023:i:c:s0167715222002310. 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.