  In this paper we study a Markovian two-dimensional bounded-variation
stochastic control problem whose state process consists of a diffusive
mean-reverting component and of a purely controlled one. The main problem's
characteristic lies in the interaction of the two components of the state
process: the mean-reversion level of the diffusive component is an affine
function of the current value of the purely controlled one. By relying on a
combination of techniques from viscosity theory and free-boundary analysis, we
provide the structure of the value function and we show that it satisfies a
second-order smooth-fit principle. Such a regularity is then exploited in order
to determine a system of functional equations solved by the two monotone
continuous curves (free boundaries) that split the control problem's state
space in three connected regions. Further properties of the free boundaries are
also obtained.
