Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model
•Present an optimal control model with jump in uncertain random environments.•Propose the principle of optimality and equation of optimality to solve the model.•The optimal solutions of two kinds of optimal problems are obtained.•The optimal pricing policies and advertising strategies of an advertis...
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| Published in: | Applied mathematics and computation Vol. 407; p. 126337 |
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| Format: | Journal Article |
| Language: | English |
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15.10.2021
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | •Present an optimal control model with jump in uncertain random environments.•Propose the principle of optimality and equation of optimality to solve the model.•The optimal solutions of two kinds of optimal problems are obtained.•The optimal pricing policies and advertising strategies of an advertising problem are provided.
Randomness is an objective indeterminacy, while uncertainty is a subjective indeterminacy. As an effective methodology, chance theory is applicable for disposing of indeterminacy composing of both uncertainty and randomness. Based on chance theory, the optimal control for uncertain stochastic dynamic systems described by both a stochastic differential equation driven by the standard Wiener process and an uncertain differential equation driven by the Liu process and V−n jumps process is considered. Then the principle of optimality is presented by drawing on the dynamic programming method. Particularly, the equation of optimality is established to solve the proposed problem. Furthermore, the optimal control problems with linear and quadratic objective functions are discussed by using the obtained equation. As an application, an advertising problem is analyzed, the corresponding optimal pricing policies and advertising strategies are provided. |
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| AbstractList | •Present an optimal control model with jump in uncertain random environments.•Propose the principle of optimality and equation of optimality to solve the model.•The optimal solutions of two kinds of optimal problems are obtained.•The optimal pricing policies and advertising strategies of an advertising problem are provided.
Randomness is an objective indeterminacy, while uncertainty is a subjective indeterminacy. As an effective methodology, chance theory is applicable for disposing of indeterminacy composing of both uncertainty and randomness. Based on chance theory, the optimal control for uncertain stochastic dynamic systems described by both a stochastic differential equation driven by the standard Wiener process and an uncertain differential equation driven by the Liu process and V−n jumps process is considered. Then the principle of optimality is presented by drawing on the dynamic programming method. Particularly, the equation of optimality is established to solve the proposed problem. Furthermore, the optimal control problems with linear and quadratic objective functions are discussed by using the obtained equation. As an application, an advertising problem is analyzed, the corresponding optimal pricing policies and advertising strategies are provided. |
| ArticleNumber | 126337 |
| Author | Chen, Xin Sheng, Linxue Zhu, Yuanguo |
| Author_xml | – sequence: 1 givenname: Xin surname: Chen fullname: Chen, Xin email: xchen@njust.edu.cn organization: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China – sequence: 2 givenname: Yuanguo surname: Zhu fullname: Zhu, Yuanguo email: ygzhu@njust.edu.cn organization: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China – sequence: 3 givenname: Linxue surname: Sheng fullname: Sheng, Linxue email: njustslx@outlook.com organization: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu, China |
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| Cites_doi | 10.1007/s10700-016-9235-y 10.1080/01969722.2010.511552 10.1016/j.physa.2019.124115 10.1007/s00500-012-0935-0 10.2307/3003143 10.1080/00207727708942059 10.1007/s00500-018-3306-7 10.1002/int.21682 10.1016/S0019-9958(58)80003-0 10.1186/2195-5468-1-9 10.1016/j.orl.2018.01.004 10.1080/00207728008966998 10.1002/int.21681 10.1016/j.ins.2017.10.050 10.1007/s10700-012-9149-2 10.20852/ntmsci.2018.244 10.1007/s002450010003 10.1016/j.apm.2014.10.042 10.1007/s10700-019-09310-y 10.1057/rpm.2015.20 10.1002/asjc.1591 10.1007/s10700-010-9073-2 10.2298/CSIS120225049D 10.1002/mma.5422 10.1016/j.ejcon.2017.06.002 10.2307/2551549 |
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| SubjectTerms | Advertising model Chance theory Dynamic programming method Optimal control |
| Title | Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model |
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