A maximum principle for fully coupled controlled forward-backward stochastic difference systems of mean-field type

被引：2
作者：
Song, Teng [1 ]
Liu, Bin [2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Forward-backward stochastic difference equations; Backward stochastic difference equations; Mean-field theory; Stochastic maximum principle; Adjoint difference equation; OPTIMALITY CONDITIONS; EQUATIONS;
D O I：
10.1186/s13662-020-02640-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the optimal control problem for fully coupled forward-backward stochastic difference equations of mean-field type under weak convexity assumption. By virtue of employing a suitable product rule and formulating a mean-field backward stochastic difference equation, we establish the stochastic maximum principle and also derive, under additional assumptions, that the stochastic maximum principle is also a sufficient condition. As an application, a Stackelberg game of mean-field backward stochastic difference equation is presented to demonstrate our results.
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页数：24
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