Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation cost functional LQ system is derived by technique Itô’s formula with jumps. For system, we establish equivalence between open-loop (closed-loop, resp.) solvability and existence an adapted solution to corresponding forward-backward differential equation constraint. ( i.e. , a regular Riccati equations). Also, analyze interrelationship strongly equations uniform convexity functional. Finally, present example which solvable but not closed-loop solvable.