IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/283418.html
   My bibliography  Save this article

A Variational Formula for Nonzero-Sum Stochastic Differential Games of FBSDEs and Applications

Author

Listed:
  • Maoning Tang

Abstract

A nonzero-sum stochastic differential game problem is investigated for fully coupled forward-backward stochastic differential equations (FBSDEs in short) where the control domain is not necessarily convex. A variational formula for the cost functional in a given spike perturbation direction of control processes is derived by the Hamiltonian and associated adjoint systems. As an application, a global stochastic maximum principle of Pontryagin’s type for open-loop Nash equilibrium points is established. Finally, an example of a linear quadratic nonzero-sum game problem is presented to illustrate that the theories may have interesting practical applications and the corresponding Nash equilibrium point is characterized by the optimality system. Here the optimality system is a fully coupled FBSDE with double dimensions (DFBSDEs in short) which consists of the state equation, the adjoint equation, and the optimality conditions.

Suggested Citation

  • Maoning Tang, 2014. "A Variational Formula for Nonzero-Sum Stochastic Differential Games of FBSDEs and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, April.
    • Handle: RePEc:hin:jnlmpe:283418
    DOI: 10.1155/2014/283418
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2014/283418.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2014/283418.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/283418?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
    ---><---

    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:jnlmpe:283418. 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.