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

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 [17], 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 [17] with positive-definite weights is a special case of the current paper.