A stochastic reversible investment problem on a finite-time horizon: Free boundary analysis

We study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional,time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investmentdisinvestment problem a zero-sum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diff usion reflected at the two boundaries.