Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system

<p style="text-indent:20px;">This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation cost functional M-MF-SLQ is derived using technique operators. It shown that convexity necessary finiteness problem, whereas uniform sufficient open-loop solvability problem. By considering a family uniformly convex functionals, characterization and minimizing sequence, whose convergence equivalent to constructed. We demonstrate with few examples our results can be employed tackling some financial problems such as mean-variance portfolio selection problem.</p>