Maximum Principle for Optimal Control of Mean-Field Backward Doubly SDEs with Delay

Meng Wang ()
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Meng Wang: Shandong University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 2, 24 pages

Abstract: Abstract In this paper, we study the control problems of mean-field backward doubly stochastic differential equations with delay in the form of an integral with respect to a finite regular measure. Using the standard variational method, we introduce a new type of anticipated mean-field doubly stochastic differential equations as adjoint equations and derive a necessary condition in form of the maximum principle for optimal control. Under appropriate assumptions, the sufficiency of the maximum principle is also established. Our results can be applied to a certain class of linear quadratic control problems and be used to study the mean-field game for a pension fund model with delayed surplus.

Keywords: Maximum principle; Mean-field model; Delayed system; Backward doubly stochastic differential equation; 34K35; 49K99; 93E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02624-5

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