LQ stochastic optimal control of forward-backward stochastic control system driven by Lévy process

2016 ◽  
Author(s):  
Hong Huang ◽  
Xiangrong Wang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Stochastic Control ◽  
Stochastic Optimal Control ◽  
Lévy Process ◽  
Levy Process ◽  
Stochastic Control System

scholarly journals Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Lévy Process

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hong Huang ◽  
Xiangrong Wang ◽  
Ting Hou ◽  
Lu Xu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Riccati Equation ◽  
Stochastic Control ◽  
Lévy Process ◽  
Levy Process ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Stochastic Control System ◽  
Generalized Riccati Equation

This paper analyzes one kind of linear quadratic (LQ) stochastic control problem of forward backward stochastic control system associated with Lévy process. We obtain the explicit form of the optimal control, then prove it to be unique, and get the linear feedback regulator by introducing one kind of generalized Riccati equation. Finally, we discuss the solvability of the generalized Riccati equation, and its existence and uniqueness of the solutions are proved in a special case.

scholarly journals A Necessary Condition for Optimal Control of Forward-Backward Stochastic Control System with Lévy Process in Nonconvex Control Domain Case

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hong Huang ◽  
Xiangrong Wang ◽  
Ying Li
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Lévy Process ◽  
State Constraints ◽  
Terminal State ◽  
Levy Process ◽  
Necessary Condition ◽  
Variational Technique ◽  
The Maximum Principle ◽  
Stochastic Control System

This paper analyzes one kind of optimal control problem which is described by forward-backward stochastic differential equations with Lévy process (FBSDEL). We derive a necessary condition for the existence of the optimal control by means of spike variational technique, while the control domain is not necessarily convex. Simultaneously, we also get the maximum principle for this control system when there are some initial and terminal state constraints. Finally, a financial example is discussed to illustrate the application of our result.

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