Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation
This paper first makes an attempt to investigate the near-optimal control of systems governed by fully nonlinear coupled forward-backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational principle and some basic estimates for state...
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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/10.1155/2014/361259 |
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| _version_ | 1832561419111890944 |
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| author | Maoning Tang |
| author_facet | Maoning Tang |
| author_sort | Maoning Tang |
| collection | DOAJ |
| description | This paper first makes an attempt to investigate the near-optimal control of systems
governed by fully nonlinear coupled forward-backward stochastic differential equations
(FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational
principle and some basic estimates for state processes and adjoint processes, we establish
the necessary conditions for any ε-near optimal control in a local form with an error order of exact ε1/2. Moreover, under additional convexity conditions on Hamiltonian function, we
prove that an ε-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality of order ε1/2. |
| format | Article |
| id | doaj-art-4126b51ef34a4c13904d63b9171f5c8d |
| 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-4126b51ef34a4c13904d63b9171f5c8d2025-02-03T01:25:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/361259361259Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential EquationMaoning Tang0Department of Mathematical Sciences, Huzhou University, Huzhou, Zhejiang 313000, ChinaThis paper first makes an attempt to investigate the near-optimal control of systems governed by fully nonlinear coupled forward-backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any ε-near optimal control in a local form with an error order of exact ε1/2. Moreover, under additional convexity conditions on Hamiltonian function, we prove that an ε-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality of order ε1/2.http://dx.doi.org/10.1155/2014/361259 |
| spellingShingle | Maoning Tang Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation Abstract and Applied Analysis |
| title | Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation |
| title_full | Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation |
| title_fullStr | Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation |
| title_full_unstemmed | Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation |
| title_short | Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation |
| title_sort | stochastic maximum principle of near optimal control of fully coupled forward backward stochastic differential equation |
| url | http://dx.doi.org/10.1155/2014/361259 |
| work_keys_str_mv | AT maoningtang stochasticmaximumprincipleofnearoptimalcontroloffullycoupledforwardbackwardstochasticdifferentialequation |