Abstract and Applied Analysis

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

Hui Min, Ying Peng, and Yongli Qin

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 839467, 15 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276906

Digital Object Identifier
doi:10.1155/2014/839467

Mathematical Reviews number (MathSciNet)
MR3198259

Zentralblatt MATH identifier
07023173

Citation

Min, Hui; Peng, Ying; Qin, Yongli. Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle. Abstr. Appl. Anal. 2014 (2014), Article ID 839467, 15 pages. doi:10.1155/2014/839467. https://projecteuclid.org/euclid.aaa/1412276906


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