  In this paper we study a reflected Markov-modulated Brownian motion with a
two sided reflection in which the drift, diffusion coefficient and the two
boundaries are (jointly) modulated by a finite state space irreducible
continuous time Markov chain. The goal is to compute the stationary
distribution of this Markov process, which in addition to the complication of
having a stochastic boundary can also include jumps at state change epochs of
the underlying Markov chain because of the boundary changes. We give the
general theory and then specialize to the case where the underlying Markov
chain has two states. Moreover, motivated by an application of optimal dividend
strategies, we consider the case where the lower barrier is zero and the upper
barrier is subject to control. In this case we generalized earlier results from
the case of a reflected Brownian motion to the Markov modulated case.
