Abstract
This paper concerns a global optimality principle for fully coupled mean-field control systems. Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Yε that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.
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The authors would like to thank the editors and the reviewers for their constructive comments and suggestions which helped us to improve this paper.
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This paper is supported by the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020MA032, ZR2022MA029), National Natural Science Foundation of China (Grant Nos. 12171279,72171133).
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Hao, T. A Global Optimality Principle for Fully Coupled Mean-field Control Systems. Acta Math. Appl. Sin. Engl. Ser. 40, 379–413 (2024). https://doi.org/10.1007/s10255-024-1112-9
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DOI: https://doi.org/10.1007/s10255-024-1112-9
Keywords
- optimal control
- global maximum principle
- fully coupled general mean-field FBSDE
- adjoint equation
- recursive utility