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 investment-disinvestment 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 diffusion reflected at the two boundaries.
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