IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n729636.html

Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

Author

Listed:
  • Pengju Duan
  • Min Ren
  • Shilong Fei

Abstract

This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.

Suggested Citation

  • Pengju Duan & Min Ren & Shilong Fei, 2013. "Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
  • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:729636
    DOI: 10.1155/2013/729636
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/729636
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2013/729636?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
    ---><---

    References listed on IDEAS

    as
    1. Jia, Guangyan, 2008. "A class of backward stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 231-237, February.
    2. 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.
    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. 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.
    2. 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.
    3. Fan, ShengJun, 2016. "Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1511-1552.
    4. Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
    5. Tian, Dejian & Jiang, Long & Davison, Matt, 2010. "On the existence of solutions to BSDEs with generalized uniformly continuous generators," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 903-909, May.
    6. Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.
    7. Tian, Dejian & Jiang, Long & Shi, Xuejun, 2013. "Lp solutions to backward stochastic differential equations with discontinuous generators," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 503-510.
    8. 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.
    9. Jin Ma & Ting-Kam Leonard Wong & Jianfeng Zhang, 2021. "Time-Consistent Conditional Expectation Under Probability Distortion," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1149-1180, August.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. N'zi, Modeste & Owo, Jean-Marc, 2009. "Backward doubly stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 920-926, April.
    15. Chen, Zengjing & Kulperger, Reg, 2006. "Minimax pricing and Choquet pricing," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 518-528, June.
    16. Auguste Aman, 2012. "Reflected Generalized Backward Doubly SDEs Driven by Lévy Processes and Applications," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1153-1172, December.
    17. Bandini, Elena & Fuhrman, Marco, 2017. "Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1441-1474.
    18. Li, Hanwu & Song, Yongsheng, 2025. "Backward Stochastic Differential Equations Driven by $\textit{G}$-Brownian Motion with Double Reflections," Center for Mathematical Economics Working Papers 717, Center for Mathematical Economics, Bielefeld University.
    19. Jean-François Chassagneux & Romuald Elie & Idris Kharroubi, 2015. "When terminal facelift enforces delta constraints," Finance and Stochastics, Springer, vol. 19(2), pages 329-362, April.
    20. Hyndman, Cody Blaine, 2007. "Forward-backward SDEs and the CIR model," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1676-1682, November.

    More about this item

    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:wly:jnljam:v:2013:y:2013:i:1:n:729636. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.