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

Hui Min, Ying Peng and Yongli Qin

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/839467

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:839467

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