摘要
研究了平均场倒向随重机微分方程,得到了平均场倒向重随机微分方程解的存在唯一性.基于平均场倒向重随机微分方程的解,给出了一类非局部随机偏微分方程解的概率解释.讨论了平均场倒向重随机系统的最优控制问题,建立了庞特利亚金型的最大值原理.最后讨论了一个平均场倒向重随机线性二次最优控制问题,展示了上述最大值原理的应用.
In this paper,mean-field backward doubly stochastic differential equations(MFBDSDEs in short)are introduced and studied.The existence and uniqueness of solutions for MF-BDSDEs is established.One probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations is given.A maximum principle of Pontryagin’s type is established for optimal control problems of MF-BDSDEs.Finally,one backward linear quadratic optimal control problem of mean-field type is discussed to illustrate the direct application of the maximum principle.
作者
朱庆峰
王天啸
石玉峰
ZHU Qingfeng;WANG Tianxiao;SHI Yufeng(School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics,Shandong Key Laboratory of Blockchain Finance,Jinan 250014,China;Institute for Financial Studies and School of Mathematics,Shandong University,Jinan 250100,China;School of Mathematics,Sichuan University,Chengdu 610065,China)
出处
《数学年刊（A辑）》
CSCD
北大核心
2020年第4期409-428,共20页
Chinese Annals of Mathematics
基金
国家重点研发计划(No.2018YFA0703900)
国家自然科学基金(No.11871309,No.11671229,No.11971332,No.11931011,No.71871129,No.11371226,No.11301298)
山东省自然科学基金(No.ZR2019MA013)
山东省高等教育科技计划项目(No.J17KA162)
泰山学者工程专项经费(No.tsqn20161041)项目的资助。
关键词
平均场
倒向重随机微分方程
非局部随机偏微分方程
最大值原理
线性二次最优控制
Mean-Field
Backward doubly stochastic differential equations
Nonlocal stochastic partial differential equations
Maximum principle
Linear quadratic optimal control
