Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information |
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Authors: | Heping Ma Bin Liu |
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Affiliation: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China |
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Abstract: | This paper deals with the risk‐sensitive control problem for mean‐field stochastic delay differential equations (MF‐SDDEs) with partial information. Firstly, under the assumptions that the control domain is not convex and the value function is non‐smooth, we establish a stochastic maximum principle (SMP). Then, by means of Itô's formula and some continuous dependence, we prove the existence and uniqueness results for another type of MF‐SDDEs. Meanwhile, the verification theorem for the MF‐SDDEs is obtained by using a clever construction of the Hamiltonian function. Finally, based on our verification theorem, a linear‐quadratic system is investigated and the optimal control is also derived by the stochastic filtering technique. |
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Keywords: | Stochastic maximum principle risk‐sensitive control mean‐field type stochastic delay differential equations continuous dependence theorem |
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