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

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作  者:FENG Siqi GAO Lei WANG Guangchen XIAO Hua 

机构地区:[1]School of Control Science and Engineering,Shandong University,Jinan 250061,China [2]School of Economics,Shandong University,Jinan 250100,China [3]School of Mathematics and Statistics,Shandong University,Weihai 264209,China

出  处:《Journal of Systems Science & Complexity》2024年第4期1392-1412,共21页系统科学与复杂性学报(英文版)

基  金:supported by the National Key R&D Program of China under Grant No.2022YFA1006103;the National Natural Science Foundation of China under Grant Nos.61821004,61925306,11831010,71973084,61977043;the National Science Foundation of Shandong Province under Grant Nos.ZR2019ZD42 and ZR2020ZD24。

摘  要: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 

分 类 号:O231[理学—运筹学与控制论]

 

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