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Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

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  • Hui Min
  • Ying Peng
  • Yongli Qin

Abstract

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

Suggested Citation

  • Hui Min & Ying Peng & Yongli Qin, 2014. "Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, April.
    • Handle: RePEc:hin:jnlaaa:839467
    DOI: 10.1155/2014/839467
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    Cited by:

    1. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.

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