Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle
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-fi...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/839467 |
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| _version_ | 1832560302672052224 |
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| author | Hui Min Ying Peng Yongli Qin |
| author_facet | Hui Min Ying Peng Yongli Qin |
| author_sort | Hui Min |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2a97ffad4d03422e9cfb4c32a905cd4f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2a97ffad4d03422e9cfb4c32a905cd4f2025-02-03T01:27:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/839467839467Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum PrincipleHui Min0Ying Peng1Yongli Qin2School of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaDepartment of Computer Science and Technology, Shandong University, Jinan 250101, ChinaSchool of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaWe 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.http://dx.doi.org/10.1155/2014/839467 |
| spellingShingle | Hui Min Ying Peng Yongli Qin Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle Abstract and Applied Analysis |
| title | Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle |
| title_full | Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle |
| title_fullStr | Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle |
| title_full_unstemmed | Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle |
| title_short | Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle |
| title_sort | fully coupled mean field forward backward stochastic differential equations and stochastic maximum principle |
| url | http://dx.doi.org/10.1155/2014/839467 |
| work_keys_str_mv | AT huimin fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple AT yingpeng fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple AT yongliqin fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple |