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arXiv · 2511.17023

Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs

Qingmeng Wei·Yaqi Xu
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Abstract

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.

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Qingmeng Wei, Yaqi Xu. 2025-11-21. Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs. https://arxiv.org/abs/2511.17023

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