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

被引：0
|
作者：
Teng Song
Bin Liu
机构：
[1] Huazhong University of Science and Technology,School of Mathematics and Statistics
[2] Huazhong University of Science and Technology,Hubei Key Laboratory of Engineering Modeling and Scientific Computing
来源：
Advances in Difference Equations | / 2020卷
关键词：
Forward–backward stochastic difference equations; Backward stochastic difference equations; Mean-field theory; Stochastic maximum principle; Adjoint difference equation; 49J21; 93E20; 93C55; 49K45; 49M05;
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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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