部分信息下带跳线性二次平均场类型的二人零和微分对策问题  

Linear Quadratic Mean field Type Stochastic Two personZero sum Differential Game Problem with Jumps Under Partial Information

作　　者：杨依芸 唐矛宁[2] 孟庆欣[2] YANG Yiyun;TANG Maoning;MENG Qingxin(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China;School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2022年第4期1-10,共10页Journal of Huzhou University

基　　金：国家自然科学基金项目(11871121);浙江省自然科学基金项目(LY21A01001);浙江省自然科学基金重点项目(Z22A013952).

摘　　要：讨论在部分信息下带跳线性二次平均场类型的二人零和微分对策问题,其中状态方程是由布朗运动和泊松随机鞅测度共同驱动,且包含仿射项的平均场类型的随机微分方程.通过二人零和微分对策中两个决策者的相互作用,引入两个Riccati方程,再利用经典的变分技术和配方法,建立开环鞍点的状态反馈表示和最优的对策值函数,最后通过讨论该问题的一个特例,得到其相应最优控制的反馈表示.In this paper,a class of linear quadratic mean field type stochastic two person zero sum differential games problem under partial information is discussed.The state equation containing affine terms is a SDE with jumps driven by a two dimensional Brownian motion and a Poisson stochastic martingale measure.Firstly,two Riccati equations are introduced through the interaction of two players.Secondly,by using classical variational technique and the completion of the squares approach,we obtain the explicit feedback representation of open loop saddle and the optimal game value function under partial information.Finally,a special case of the problem is discussed and the corresponding feedback representation of optimal control is obtained.

关 键 词：二人零和微分对策 线性二次 平均场 部分信息 倒向随机微分方程 开环鞍点 RICCATI方程 

分 类 号：O232[理学—运筹学与控制论]