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<p>This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from Mei et al. (ArXiv:2501.00981), the cost functionals do not have positive-definite weights here. When the problems are merely finite, we construct a sequence of asymptotic optimal controls and derive their closed-loop representations. For the solvability, an equivalence result between the open-loop and closed-loop cases is established through algebraic Riccati equations and infinite horizon backward stochastic differential equations. It can be seen that the research in Mei et al. (ArXiv:2501.00981) with positive-definite weights is a special case of the current paper.</p>

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Infinite Horizon Mean-Field Linear-Quadratic Optimal Control Problems with Switching and Indefinite-Weighted Costs

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Hongwei Mei,
  • Rui Wang,
  • Qingmeng Wei,
  • Jiongmin Yong

摘要

This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from Mei et al. (ArXiv:2501.00981), the cost functionals do not have positive-definite weights here. When the problems are merely finite, we construct a sequence of asymptotic optimal controls and derive their closed-loop representations. For the solvability, an equivalence result between the open-loop and closed-loop cases is established through algebraic Riccati equations and infinite horizon backward stochastic differential equations. It can be seen that the research in Mei et al. (ArXiv:2501.00981) with positive-definite weights is a special case of the current paper.