Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911278384021504 |
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| author | Wei, Qingmeng Xu, Yaqi |
| author_facet | Wei, Qingmeng Xu, Yaqi |
| contents | This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze fully coupled forward-backward stochastic differential equations (FBSDEs) of conditional McKean-Vlasov type with Markovian switching and establish its well-posedness under a generalized domination-monotonicity condition. Building upon this solvability result, we then derive necessary and sufficient conditions for both the open-loop optimal control in the control problem and the mean-field Nash equilibria in the game problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs Wei, Qingmeng Xu, Yaqi Optimization and Control This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze fully coupled forward-backward stochastic differential equations (FBSDEs) of conditional McKean-Vlasov type with Markovian switching and establish its well-posedness under a generalized domination-monotonicity condition. Building upon this solvability result, we then derive necessary and sufficient conditions for both the open-loop optimal control in the control problem and the mean-field Nash equilibria in the game problem. |
| title | Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.17023 |