Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916547591667712 |
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| author | Mei, Hongwei Wei, Qingmeng Yong, Jiongmin |
| author_facet | Mei, Hongwei Wei, Qingmeng Yong, Jiongmin |
| contents | This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has been adopted. Desired algebraic Riccati equations (AREs, for short) and a system of backward stochastic differential equations (BSDEs, for short) in infinite time horizon with the coefficients depending on the Markov chain have been derived. The determination of closed-loop optimal strategy follows from the solvability of ARE and BSDE. Moreover, the solvability of BSDEs leads to a characterization of open-loop solvability of the optimal control problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching Mei, Hongwei Wei, Qingmeng Yong, Jiongmin Optimization and Control 93E20, 49N10, 60F17 This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has been adopted. Desired algebraic Riccati equations (AREs, for short) and a system of backward stochastic differential equations (BSDEs, for short) in infinite time horizon with the coefficients depending on the Markov chain have been derived. The determination of closed-loop optimal strategy follows from the solvability of ARE and BSDE. Moreover, the solvability of BSDEs leads to a characterization of open-loop solvability of the optimal control problem. |
| title | Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching |
| topic | Optimization and Control 93E20, 49N10, 60F17 |
| url | https://arxiv.org/abs/2501.00981 |