A maximum principle for fully coupled stochastic control systems of mean-field type |
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Authors: | Ruijing Li Bin Liu |
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Institution: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China |
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Abstract: | The present paper considers an optimal control problem for fully coupled forward–backward stochastic differential equations (FBSDEs) of mean-field type in the case of controlled diffusion coefficient. Moreover, the control domain is not assumed to be convex. By virtue of a reduction method, we establish the necessary optimality conditions of Pontryagin's type. As an application, a linear–quadratic stochastic control problem is studied. |
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Keywords: | Forward&ndash backward stochastic differential equations Mean-field SDE Maximum principle Adjoint equation Ekeland's variational principle |
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