IDEAS home Printed from https://ideas.repec.org/a/hin/jnijsa/402830.html
   My bibliography  Save this article

Reflected forward-backward SDE s and obstacle problems with boundary conditions

Author

Listed:
  • Jin Ma
  • Jakša Cvitanić

Abstract

In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short). More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem) with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option .

Suggested Citation

  • Jin Ma & Jakša Cvitanić, 2001. "Reflected forward-backward SDE s and obstacle problems with boundary conditions," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-26, January.
    • Handle: RePEc:hin:jnijsa:402830
    DOI: 10.1155/S1048953301000090
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJSA/14/402830.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJSA/14/402830.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S1048953301000090?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhen-Qing Chen & Xinwei Feng, 2021. "Reflected Backward Stochastic Differential Equation with Rank-Based Data," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1213-1247, September.
    2. Qikang Ran & Tusheng Zhang, 2010. "Existence and Uniqueness of Bounded Weak Solutions of a Semilinear Parabolic PDE," Journal of Theoretical Probability, Springer, vol. 23(4), pages 951-971, December.

    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:hin:jnijsa:402830. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.