A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis |
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Authors: | Tiziano De Angelis Giorgio Ferrari |
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Institution: | 1. School of Mathematics, University of Manchester, Oxford Road, M13 9PL Manchester, UK;2. Center for Mathematical Economics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, Germany |
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Abstract: | We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, 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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Keywords: | 93E20 60G40 35R35 91A15 91B70 |
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