The mean-field control problem for heterogeneous forward-backward systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908842819846144 |
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| author | Sojmark, Andreas Zhang, Zeng |
| author_facet | Sojmark, Andreas Zhang, Zeng |
| contents | We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel methodology for reducing the well-posedness of such systems to that of a single randomized mean-field FBSDE. As a consequence, we show that, in the fully coupled case, smallness conditions yield existence and uniqueness for both the system itself and the associated variational and adjoint systems. Secondly, we derive a stochastic maximum principle and a verification for the mean-field control problem. This provides necessary and sufficient conditions for optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The mean-field control problem for heterogeneous forward-backward systems Sojmark, Andreas Zhang, Zeng Optimization and Control Probability 49N80, 60H10, 60K35, 93E20 We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel methodology for reducing the well-posedness of such systems to that of a single randomized mean-field FBSDE. As a consequence, we show that, in the fully coupled case, smallness conditions yield existence and uniqueness for both the system itself and the associated variational and adjoint systems. Secondly, we derive a stochastic maximum principle and a verification for the mean-field control problem. This provides necessary and sufficient conditions for optimality. |
| title | The mean-field control problem for heterogeneous forward-backward systems |
| topic | Optimization and Control Probability 49N80, 60H10, 60K35, 93E20 |
| url | https://arxiv.org/abs/2602.17879 |