A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lévy Process with Terminal State Constraints

2017 ◽  
Vol 31 (4) ◽  
pp. 859-874 ◽  
Author(s):  
Hong Huang ◽  
Xiangrong Wang ◽  
Meijuan Liu
Keyword(s):  
Control System ◽  
Maximum Principle ◽  
Stochastic Control ◽  
Lévy Process ◽  
State Constraints ◽  
Terminal State ◽  
Levy Process ◽  
Stochastic Control System ◽  
Fully Coupled

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.

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 Maximum Principle for Forward-Backward Stochastic Control System Driven by Lévy Process

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangrong Wang ◽  
Hong Huang
Keyword(s):  
Maximum Principle ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
Levy Process ◽  
Linear Quadratic ◽  
Controlled System ◽  
The Maximum Principle ◽  
Stochastic Control System ◽  
Continuity Result ◽  
Stochastic Optimal Control Problem

We study a stochastic optimal control problem where the controlled system is described by a forward-backward stochastic differential equation driven by Lévy process. In order to get our main result of this paper, the maximum principle, we prove the continuity result depending on parameters about fully coupled forward-backward stochastic differential equations driven by Lévy process. Under some additional convexity conditions, the maximum principle is also proved to be sufficient. Finally, the result is applied to the linear quadratic problem.

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