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Connection between MP and DPP for Mean-Field Stochastic Optimal Control Problems

  • Guangzhi Cui
  • Tianyang Nie
  • Guangchen Wang
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Abstract

This paper deals with the optimal control problem for the general mean-field stochastic differential equations, in which the coefficients depend on both the state process as well as on its law. We focus on the connection between the general maximum principle and the dynamic programming principle for such a control problem. We establish the relationship between the value function of the mean-field optimal control problem and the adjoint equations in the maximum principle. We also give a general mean-field stochastic verification theorem. Some examples are solved explicitly to illustrate our results.

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Cite

BibTeXRIS
BibTeX
@misc{cui2026connection,
  title = {{Connection between MP and DPP for Mean-Field Stochastic Optimal Control Problems}},
  author = {Guangzhi Cui and Tianyang Nie and Guangchen Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18437},
  eprint = {2610.18437},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18437},
}
RIS
TY  - UNPB
TI  - Connection between MP and DPP for Mean-Field Stochastic Optimal Control Problems
AU  - Guangzhi Cui
AU  - Tianyang Nie
AU  - Guangchen Wang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18437
UR  - https://arxiv.org/abs/2610.18437
AB  - This paper deals with the optimal control problem for the general mean-field stochastic differential equations, in which the coefficients depend on both the state process as well as on its law. We focus on the connection between the general maximum principle and the dynamic programming principle for such a control problem. We establish the relationship between the value function of the mean-field optimal control problem and the adjoint equations in the maximum principle. We also give a general mean-field stochastic verification theorem. Some examples are solved explicitly to illustrate our results.
ER  -