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, 1-15

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:839467

DOI: 10.1155/2014/839467

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