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Maximum Principle for stochastic Control System with Elephant Memory and Jump Diffusion

Journal of Systems Science & Complexity 2024年第4期37卷 1392-1412页

作者： FENG Siqi GAO Lei WANG Guangchen XIAO Hua School of Control Science and Engineering Shandong University School of Economics Shandong University School of Mathematics and Statistics Shandong University

Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated backward stochastic differential equation, derive a stochastic maximum principle,and prove a verification theorem for the aforementioned optimal control problem. Furthermore, the authors generalize these results to nonzero-sum stochastic differential game problems. Finally, the authors apply the theoretical results to the duopoly game problem and obtain the corresponding Nash equilibrium solution.

关键词： anticipated backward stochastic differential equation elephant memory Fréchet derivative maximum principle stochastic delayed differential equation

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A General Comparison Theorem for 1-dimensional anticipated BSDEs

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 343-348页

作者： Xiao-ming XU Institute of Finance and Statistics School of Mathematical Sciences Nanjing Normal University

anticipated backward stochastic differential equation （ABSDE） studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for ABSDEs.

关键词： anticipated backward stochastic differential equation backward stochastic differential equation comparison theorem

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The Quadratic Problem for stochastic Linear Control Systems with Delay

The Quadratic Problem for Stochastic Linear Control Systems ...

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第三十届中国控制会议

作者： CHEN Li~1,WU Zhen~2 1.Department of Mathematics,China University of Mining and Technology,Beijing 100083,P.R.China 2.Corresponding author.School of Mathematics,Shandong University,Jinan 250100,P.R.China

＜正＞In this paper,we discuss the optimal control for stochastic linear system with delay in state and control variables and a quadratic criterion.This problem will lead to a kind of generalized forward-backward stochastic differential equations（FBSDEs） with Ito stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations.Especially,we present the optimal feedback regulator for the system with time delay in control input via two different methods.

关键词： stochastic delay differential equation anticipated backward stochastic differential equation Forward-backward stochastic differential equation Linear-quadratic stochastic optimal control with delay

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