A Mean-Field Optimal Control for Fully Coupled Forward-Backward Stochastic Control Systems with Lévy Processes  

作　　者：HUANG Zhen WANG Ying WANG Xiangrong 

机构地区：[1]College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China.

出　　处：《Journal of Systems Science & Complexity》2022年第1期205-220,共16页系统科学与复杂性学报（英文版）

基　　金：supported by the Major Basic Research Program of Natural Science Foundation of Shandong Province under Grant No.2019A01;the Natural Science Foundation of Shandong Province of China under Grant No.ZR2020MF062。

摘　　要：This paper is concerned with a class of mean-field type stochastic optimal control systems,which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy processes.In these systems,the coefficients contain not only the state processes but also their marginal distribution,and the cost function is of mean-field type as well.The necessary and sufficient conditions for such optimal problems are obtained.Furthermore,the applications to the linear quadratic stochastic optimization control problem are investigated.

关 键 词：Adjoint equation Lévy processes mean-field forward-backward stochastic differential equations stochastic maximum principle Teugels martingales 

分 类 号：O211.6[理学—概率论与数理统计] O232[理学—数学]