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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |