IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v106y2015icp73-81.html
   My bibliography  Save this article

Mean-field backward stochastic differential equations with subdifferential operator and its applications

Author

Listed:
  • Lu, Wen
  • Ren, Yong
  • Hu, Lanying

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations with subdifferential operator corresponding to a lower semi-continuous convex function. By means of Yosida approximation, the existence and uniqueness of the solution is established. As an application, we give a probability interpretation for the viscosity solutions of a class of nonlocal parabolic variational inequalities.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:73-81
    DOI: 10.1016/j.spl.2015.06.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215002187
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2015.06.022?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. Maticiuc, Lucian & Rascanu, Aurel, 2010. "A stochastic approach to a multivalued Dirichlet-Neumann problem," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 777-800, June.
    2. Ahmed, N. U. & Ding, X., 1995. "A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 65-85, November.
    3. 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.
    4. Pardoux, Etienne & Rascanu, Aurel, 1998. "Backward stochastic differential equations with subdifferential operator and related variational inequalities," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 191-215, August.
    5. 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.
    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. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    2. 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.
    3. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    4. 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.
    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. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2015. "Multivalued backward stochastic differential equations with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3170-3195.
    7. Eduard Rotenstein, 2008. "Pricing financial derivatives by a minimizing method," Papers 0811.4613, arXiv.org, revised Oct 2013.
    8. 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.
    9. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    10. Confortola, Fulvia, 2007. "Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 613-628, May.
    11. 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).
    12. 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.
    13. Bensoussan, Alain & Li, Yiqun & Yam, Sheung Chi Phillip, 2018. "Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 644-688.
    14. Cordoni, Francesco & Di Persio, Luca & Maticiuc, Lucian & Zălinescu, Adrian, 2020. "A stochastic approach to path-dependent nonlinear Kolmogorov equations via BSDEs with time-delayed generators and applications to finance," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1669-1712.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:106:y:2015:i:c:p:73-81. 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.