A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type
Abstract 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,...
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SpringerOpen
2020-04-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02640-x |
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doaj-52f390f785ea48d2be91474c22eba0c62020-11-25T02:11:11ZengSpringerOpenAdvances in Difference Equations1687-18472020-04-012020112410.1186/s13662-020-02640-xA maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field typeTeng Song0Bin Liu1School of Mathematics and Statistics, Huazhong University of Science and TechnologyHubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and TechnologyAbstract 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.http://link.springer.com/article/10.1186/s13662-020-02640-xForward–backward stochastic difference equationsBackward stochastic difference equationsMean-field theoryStochastic maximum principleAdjoint difference equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Teng Song Bin Liu |
| spellingShingle |
Teng Song Bin Liu A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type Advances in Difference Equations Forward–backward stochastic difference equations Backward stochastic difference equations Mean-field theory Stochastic maximum principle Adjoint difference equation |
| author_facet |
Teng Song Bin Liu |
| author_sort |
Teng Song |
| title |
A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| title_short |
A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| title_full |
A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| title_fullStr |
A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| title_full_unstemmed |
A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| title_sort |
maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-04-01 |
| description |
Abstract 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. |
| topic |
Forward–backward stochastic difference equations Backward stochastic difference equations Mean-field theory Stochastic maximum principle Adjoint difference equation |
| url |
http://link.springer.com/article/10.1186/s13662-020-02640-x |
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