Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions
We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/761306 |
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| _version_ | 1832554203681128448 |
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| author | Yan Wang Aimin Song Cheng-De Zheng Enmin Feng |
| author_facet | Yan Wang Aimin Song Cheng-De Zheng Enmin Feng |
| author_sort | Yan Wang |
| collection | DOAJ |
| description | We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game. Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example. |
| format | Article |
| id | doaj-art-1bc2778c54c4486da68611d06ad80df4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1bc2778c54c4486da68611d06ad80df42025-02-03T05:52:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/761306761306Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump DiffusionsYan Wang0Aimin Song1Cheng-De Zheng2Enmin Feng3School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, ChinaSchool of Science, Dalian Jiaotong University, Dalian 116028, ChinaSchool of Science, Dalian Jiaotong University, Dalian 116028, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116023, ChinaWe consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game. Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.http://dx.doi.org/10.1155/2013/761306 |
| spellingShingle | Yan Wang Aimin Song Cheng-De Zheng Enmin Feng Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions Abstract and Applied Analysis |
| title | Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions |
| title_full | Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions |
| title_fullStr | Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions |
| title_full_unstemmed | Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions |
| title_short | Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions |
| title_sort | nonzero sum stochastic differential game between controller and stopper for jump diffusions |
| url | http://dx.doi.org/10.1155/2013/761306 |
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