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

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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Main Authors: Hui Min, Ying Peng, Yongli Qin
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/839467
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spelling doaj-2a97ffad4d03422e9cfb4c32a905cd4f2020-11-24T22:05:06ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Hui Min
Ying Peng
Yongli Qin
spellingShingle Hui Min
Ying Peng
Yongli Qin
Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle
Abstract and Applied Analysis
author_facet Hui Min
Ying Peng
Yongli Qin
author_sort Hui Min
title 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_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_sort fully coupled mean-field forward-backward stochastic differential equations and stochastic maximum principle
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
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.
url http://dx.doi.org/10.1155/2014/839467
work_keys_str_mv AT huimin fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple
AT yingpeng fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple
AT yongliqin fullycoupledmeanfieldforwardbackwardstochasticdifferentialequationsandstochasticmaximumprinciple
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