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 Control System Driven by Itô-Lévy Processes under Initial-Terminal Constraints

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Meijuan Liu ◽  
Xiangrong Wang ◽  
Hong Huang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Control Variable ◽  
Terminal State ◽  
Necessary Condition ◽  
Utility Optimization ◽  
Terminal Constraints ◽  
Stochastic Optimal Control Problem ◽  
Backward Control ◽  
Existence Of Optimal Control

This paper investigates a stochastic optimal control problem where the control system is driven by Itô-Lévy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.

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.

scholarly journals A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Shaolin Ji ◽  
Qingmeng Wei ◽  
Xiumin Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Differential Equation ◽  
State Constraints ◽  
Terminal State ◽  
Necessary Condition ◽  
Variation Principle ◽  
Linear Quadratic ◽  
Doubly Stochastic

We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

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