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This paper investigates the stochastic linear quadratic (LQ, for short)optimal control problem of Markov regime switching system. The representationof the cost functional for the stochastic LQ optimal control problem of Markovregime switching system is derived using the technique of It{\^o}'s formula.For the stochastic LQ optimal control problem of Markov regime switchingsystem, we establish the equivalence between the open-loop (closed-loop)solvability and the existence of an adapted solution to the correspondingforward-backward stochastic differential equation with constraint (theexistence of a regular solution to the Riccati equation). Also, we analyze theinterrelationship between the strongly regular solvability of the Riccatiequation and the uniform convexity of the cost functional.

Open-Loop and Closed-Loop Solvabilities for Stochastic Linear Quadratic Optimal Control Problems of Markov Regime-Switching System