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

42 Pages Posted: 8 Sep 2013 Last revised: 29 Nov 2013

See all articles by Tiziano De Angelis

Tiziano De Angelis

University of Manchester

Giorgio Ferrari

Bielefeld University - Center for Mathematical Economics

Date Written: April 8, 2013

Abstract

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 one-dimensional, time-homogeneous, linear diff usion 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 di ffusion reflected at the two boundaries.

Keywords: reversible investment, singular stochastic control, zero-sum optimal stopping games, free boundary problems, Skorokhod reflection problem

JEL Classification: C02, C73, E22, D92

Suggested Citation

De Angelis, Tiziano and Ferrari, Giorgio, A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis (April 8, 2013). Institute of Mathematical Economics Working Paper No. 477, Available at SSRN: https://ssrn.com/abstract=2289963 or http://dx.doi.org/10.2139/ssrn.2289963

Tiziano De Angelis

University of Manchester ( email )

Oxford Rd. M13 9PL
Manchester
United Kingdom

Giorgio Ferrari (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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