Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929736477835264 |
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| author | Xiong, Jie Xu, Wen Yang, Ying |
| author_facet | Xiong, Jie Xu, Wen Yang, Ying |
| contents | In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique solvability of the optimality system for this control problem through the variational method. Subsequently, we reformulate the mean-field linear-quadratic (MF-BSLQ) problem as a constrained BSDE control problem by imposing constraints on the expectation processes, which we solve using the Extended Lagrange multiplier method. Finally, we derive an explicit expression for the optimal control associated with Problem (MF-BSLQ). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients Xiong, Jie Xu, Wen Yang, Ying Optimization and Control In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique solvability of the optimality system for this control problem through the variational method. Subsequently, we reformulate the mean-field linear-quadratic (MF-BSLQ) problem as a constrained BSDE control problem by imposing constraints on the expectation processes, which we solve using the Extended Lagrange multiplier method. Finally, we derive an explicit expression for the optimal control associated with Problem (MF-BSLQ). |
| title | Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.00369 |