  In this paper, we investigate the open-loop and weak closed-loop
solvabilities of stochastic linear quadratic (LQ, for short) optimal control
problem of Markovian regime switching system. Interestingly, these two
solvabilities are equivalent. We first provide an alternative characterization
of the open-loop solvability of the LQ problem using the perturbation approach.
Then, we study the weak closed-loop solvability of the LQ problem of Markovian
regime switching system, and establish the equivalent relationship between
open-loop and weak closed-loop solvabilities. Finally, we present an example to
illustrate the procedure for finding weak closed-loop optimal strategies within
the framework of Markovian regime switching system.
