scholarly journals Optimal Control Problems of Fully Coupled FBSDEs and Viscosity Solutions of Hamilton--Jacobi--Bellman Equations

2014 ◽  
Vol 52 (3) ◽  
pp. 1622-1662 ◽  
Author(s):  
Juan Li ◽  
Qingmeng Wei
Keyword(s):  
Optimal Control ◽  
Viscosity Solutions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Fully Coupled

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

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Min ◽  
Ying Peng ◽  
Yongli Qin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Maximum Principles ◽  
Control Problems ◽  
Linear Quadratic Optimal Control ◽  
Fully Coupled

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.

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