Recursive impulse control problem with Markov-switching and viscosity solution of HJB equation

In this work, a Markov-switching recursive stochastic optimal control problem with impulse controls is studied. The main feature of this problem is that the cost functional is stated as the solution of a regime-switching backward stochastic differential equation with impulse controls. The existence and uniqueness of the viscosity solution of the Hamilton-Jacobi-Bellman equation with obstacles is established via the dynamic programming principle.