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.
|Date of creation:||30 Apr 2014|
|Contact details of provider:|| Postal: Postfach 10 01 31, 33501 Bielefeld|
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Maria B. Chiarolla & Giorgio Ferrari, 2011. "Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem," Papers 1108.4886, arXiv.org, revised Dec 2013.
- Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
- Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012.
"Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources,"
1203.3757, arXiv.org, revised Aug 2013.
- Chiarolla, Maria B. & Ferrari, Giorgio & Riedel, Frank, 2014. "Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources," Center for Mathematical Economics Working Papers 463, Center for Mathematical Economics, Bielefeld University.
- Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 581-593.
- Xia Su & Frank Riedel, 2006.
"On Irreversible Investment,"
Bonn Econ Discussion Papers
bgse13_2006, University of Bonn, Germany.
- Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
- Ferrari, Giorgio, 2014.
"On an integral equation for the free boundary of stochastic, irreversible investment problems,"
Center for Mathematical Economics Working Papers
471, Center for Mathematical Economics, Bielefeld University.
- Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
- Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
- Samuel Bentolila & Giuseppe Bertola, 1990. "Firing Costs and Labour Demand: How Bad is Eurosclerosis?," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 381-402.
- Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, 04.
When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:477. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bettina Weingarten)
If references are entirely missing, you can add them using this form.