Fully coupled mean-field forward-backward stochastic differential equations and stochastic maximum principle
type: Item
instance of: scholarly article
title: Fully coupled mean-field forward-backward stochastic differential equations and stochastic maximum principle
zbMATH Open document ID: 1474.49053
DOI: 10.1155/2014/839467
author: Hui Min
author: Ying Peng
author: Yongli Qin
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 7023173
Wikidata QID: Q59041934
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/839467
OpenAlex ID: W2036330223
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description: scientific article; zbMATH DE number 7023173