Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
We get a new type of controlled backward stochastic differential equations (BSDEs), namely, the BSDEs, coupled with value function. We prove the existence and the uniqueness theorem as well as a comparison theorem for such BSDEs coupled with value function by using the approximation method. We get t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/262713 |
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| _version_ | 1832561102560428032 |
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| author | Tao Hao Juan Li |
| author_facet | Tao Hao Juan Li |
| author_sort | Tao Hao |
| collection | DOAJ |
| description | We get a new type of controlled backward stochastic differential equations (BSDEs), namely, the BSDEs, coupled with value function. We prove the existence and the uniqueness theorem as well as a comparison theorem for such BSDEs coupled with value function by using the approximation method. We get the related dynamic programming principle (DPP) with the help of the stochastic backward semigroup which was introduced by Peng in 1997. By making use of a new, more direct approach, we prove that our nonlocal Hamilton-Jacobi-Bellman (HJB) equation has a unique viscosity solution in the space of continuous functions of at most polynomial growth. These results generalize the corresponding conclusions given by Buckdahn et al. (2009) in the case without control. |
| format | Article |
| id | doaj-art-90bf0eee7c6642e3be326dc8120c2ca9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-90bf0eee7c6642e3be326dc8120c2ca92025-02-03T01:25:54ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/262713262713Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control ProblemsTao Hao0Juan Li1School of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaSchool of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaWe get a new type of controlled backward stochastic differential equations (BSDEs), namely, the BSDEs, coupled with value function. We prove the existence and the uniqueness theorem as well as a comparison theorem for such BSDEs coupled with value function by using the approximation method. We get the related dynamic programming principle (DPP) with the help of the stochastic backward semigroup which was introduced by Peng in 1997. By making use of a new, more direct approach, we prove that our nonlocal Hamilton-Jacobi-Bellman (HJB) equation has a unique viscosity solution in the space of continuous functions of at most polynomial growth. These results generalize the corresponding conclusions given by Buckdahn et al. (2009) in the case without control.http://dx.doi.org/10.1155/2014/262713 |
| spellingShingle | Tao Hao Juan Li Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems Abstract and Applied Analysis |
| title | Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems |
| title_full | Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems |
| title_fullStr | Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems |
| title_full_unstemmed | Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems |
| title_short | Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems |
| title_sort | backward stochastic differential equations coupled with value function and related optimal control problems |
| url | http://dx.doi.org/10.1155/2014/262713 |
| work_keys_str_mv | AT taohao backwardstochasticdifferentialequationscoupledwithvaluefunctionandrelatedoptimalcontrolproblems AT juanli backwardstochasticdifferentialequationscoupledwithvaluefunctionandrelatedoptimalcontrolproblems |