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

Tiziano De Angelis and Giorgio Ferrari

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 4080-4119

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.

Keywords: Partially reversible investment; Singular stochastic control; Zero-sum optimal stopping games; Free-boundary problems; Skorokhod reflection problem (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:12:p:4080-4119

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DOI: 10.1016/j.spa.2014.07.008

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