Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations
In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and t...
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2898 |
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| author | Li Chen Peipei Zhou Hua Xiao |
| author_facet | Li Chen Peipei Zhou Hua Xiao |
| author_sort | Li Chen |
| collection | DOAJ |
| description | In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered. |
| first_indexed | 2024-03-11T01:34:54Z |
| format | Article |
| id | doaj.art-1916856b66a14e9ca90038ecabc61740 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:34:54Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1916856b66a14e9ca90038ecabc617402023-11-18T17:02:57ZengMDPI AGMathematics2227-73902023-06-011113289810.3390/math11132898Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential EquationsLi Chen0Peipei Zhou1Hua Xiao2School of Science, China University of Mining and Technology, Beijing 100083, ChinaSchool of Science, China University of Mining and Technology, Beijing 100083, ChinaSchool of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaIn this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered.https://www.mdpi.com/2227-7390/11/13/2898Stackelberg gamestate delayforward–backward stochastic differential equationlinear–quadratic problem |
| spellingShingle | Li Chen Peipei Zhou Hua Xiao Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations Mathematics Stackelberg game state delay forward–backward stochastic differential equation linear–quadratic problem |
| title | Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations |
| title_full | Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations |
| title_fullStr | Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations |
| title_full_unstemmed | Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations |
| title_short | Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations |
| title_sort | backward stackelberg games with delay and related forward backward stochastic differential equations |
| topic | Stackelberg game state delay forward–backward stochastic differential equation linear–quadratic problem |
| url | https://www.mdpi.com/2227-7390/11/13/2898 |
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