IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v355y2019icp282-298.html
   My bibliography  Save this article

Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

Author

Listed:
  • Douissi, Soukaina
  • Wen, Jiaqiang
  • Shi, Yufeng

Abstract

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H > 1/2. First, the existence and uniqueness of this new type of BSDEs are established using two different approaches. Then, a comparison theorem for such BSDEs is obtained. Finally, as an application of this type of equations, a related stochastic optimal control problem is studied.

Suggested Citation

  • Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:282-298
    DOI: 10.1016/j.amc.2019.02.072
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301821
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.072?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. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    3. Wen, Jiaqiang & Shi, Yufeng, 2017. "Anticipative backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 118-127.
    4. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    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. 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).
    2. Kyong-Il, Ri & Myong-Guk, Sin, 2024. "Existence and uniqueness of solution for fully coupled fractional forward–backward stochastic differential equations with delay and anticipated term," Statistics & Probability Letters, Elsevier, vol. 206(C).
    3. Pei Zhang & Adriana Irawati Nur Ibrahim & Nur Anisah Mohamed, 2023. "Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator," Mathematics, MDPI, vol. 11(23), pages 1-13, December.
    4. Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    5. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).

    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. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    2. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    3. Pei Zhang & Adriana Irawati Nur Ibrahim & Nur Anisah Mohamed, 2023. "Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator," Mathematics, MDPI, vol. 11(23), pages 1-13, December.
    4. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    5. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    6. Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    7. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations with subdifferential operator and its applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 73-81.
    8. 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).
    9. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    10. Yu, Xianye & Zhang, Mingbo, 2020. "Backward stochastic differential equations driven by fractional noise with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 159(C).
    11. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations in general probability spaces," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 1-11.
    12. Wen, Jiaqiang & Shi, Yufeng, 2017. "Anticipative backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 118-127.
    13. Alexander Aurell, 2018. "Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations," Games, MDPI, vol. 9(4), pages 1-26, November.
    14. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    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. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    17. Mingyu Xu, 2007. "Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1005-1039, December.
    18. Li, Hanwu, 2024. "Backward stochastic differential equations with double mean reflections," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    19. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    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:apmaco:v:355:y:2019:i:c:p:282-298. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.