Stochastic Maximum Principle for Generalized Mean-Field Delay Control Problem

Hancheng Guo (), Jie Xiong () and Jiayu Zheng ()
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Hancheng Guo: University of Macau
Jie Xiong: Southern University of Science and Technology
Jiayu Zheng: Shenzhen MSU-BIT University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 14, 352-377

Abstract: Abstract In this paper, we first derive the existence and uniqueness theorems for solutions to a class of generalized mean-field delay stochastic differential equations and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-field delay control problem. Since the state equation is distribution-depending, we define the adjoint equation as a MFABSDE in which all the derivatives of the coefficients are in Lions’ sense. We also provide a sufficient condition for the optimality of the control.

Keywords: Existence and uniqueness; Stochastic maximum principle; Mean-field control problem; McKean–Vlasov equation; Lions derivative; 93E20; 93E03; 60H10; 60H30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02398-2

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