Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913880911904768 |
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| author | Kharroubi, Idris Mekkaoui, Samy Pham, Huyên |
| author_facet | Kharroubi, Idris Mekkaoui, Samy Pham, Huyên |
| contents | We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccati equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_05595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic maximum principle for optimal control problem of non exchangeable mean field systems Kharroubi, Idris Mekkaoui, Samy Pham, Huyên Optimization and Control Probability 49N80, 60K35, 93E20 We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccati equations. |
| title | Stochastic maximum principle for optimal control problem of non exchangeable mean field systems |
| topic | Optimization and Control Probability 49N80, 60K35, 93E20 |
| url | https://arxiv.org/abs/2506.05595 |