Before revision:  We show that, if the drift is positive in each regime , it is optimal to adopt a barrier strategy at certain positive regime-dependent levels, and explicitly characterize the value function as the fixed point of a contraction.
After revision:  We show that, if the drift is positive in each state , it is optimal to adopt a barrier strategy at certain positive regime-dependent levels, and explicitly characterize the value function as the fixed point of a contraction.