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Solvability of forward–backward stochastic partial differential equations

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  • Yin, Hong

Abstract

In this paper we study the solvability of a class of fully-coupled forward–backward stochastic partial differential equations (FBSPDEs). These FBSPDEs cannot be put into the framework of stochastic evolution equations in general, and the usual decoupling methods for the Markovian forward–backward SDEs are difficult to apply. We prove the well-posedness of the FBSPDEs, under various conditions on the coefficients, by using either the method of contraction mapping or the method of continuation. These conditions, especially in the higher dimensional case, are novel in the literature.

Suggested Citation

  • Yin, Hong, 2014. "Solvability of forward–backward stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2583-2604.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2583-2604
    DOI: 10.1016/j.spa.2014.03.005
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    References listed on IDEAS

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    1. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    2. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
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    Cited by:

    1. Bo Yan & Yanping Liu & Si Liu, 2023. "Corporate social responsibility in long‐term supply chain management," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(1), pages 17-27, January.

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