A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis

de Angelis T, Ferrari G (2013) Center for Mathematical Economics Working Papers; 477.
Bielefeld: Center for Mathematical Economics.

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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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de Angelis T, Ferrari G. A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis. Center for Mathematical Economics Working Papers. Vol 477. Bielefeld: Center for Mathematical Economics; 2013.
de Angelis, T., & Ferrari, G. (2013). A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis (Center for Mathematical Economics Working Papers, 477). Bielefeld: Center for Mathematical Economics.
de Angelis, T., and Ferrari, G. (2013). A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis. Center for Mathematical Economics Working Papers, 477, Bielefeld: Center for Mathematical Economics.
de Angelis, T., & Ferrari, G., 2013. A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis, Center for Mathematical Economics Working Papers, no.477, Bielefeld: Center for Mathematical Economics.
T. de Angelis and G. Ferrari, A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis, Center for Mathematical Economics Working Papers, vol. 477, Bielefeld: Center for Mathematical Economics, 2013.
de Angelis, T., Ferrari, G.: A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis. Center for Mathematical Economics Working Papers, 477. Center for Mathematical Economics, Bielefeld (2013).
de Angelis, Tiziano, and Ferrari, Giorgio. A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis. Bielefeld: Center for Mathematical Economics, 2013. Center for Mathematical Economics Working Papers. 477.
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