Optimal partially reversible investment with entry decision and general production function
AbstractThis paper studies the problem of a company that adjusts its stochastic production capacity in reversible investments with controls of expansion and contraction. The company may also decide on the activation time of its production. The profit production function is of a very general form satisfying minimal standard assumptions. The objective of the company is to find an optimal entry and production decision to maximize its expected total net profit over an infinite time horizon. The resulting dynamic programming principle is a two-step formulation of a singular stochastic control problem and an optimal stopping problem. The analysis of value functions relies on viscosity solutions of the associated Bellman variational inequations. We first state several general properties and in particular smoothness results on the value functions. We then provide a complete solution with explicit expressions of the value functions and the optimal controls: the company activates its production once a fixed entry-threshold of the capacity is reached, and invests in capital so as to maintain its capacity in a closed bounded interval. The boundaries of these regions can be computed explicitly and their behavior is studied in terms of the parameters of the model.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 115 (2005)
Issue (Month): 5 (May)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Timothy C. Johnson & Mihail Zervos, 2010. "The explicit solution to a sequential switching problem with non-smooth data," LSE Research Online Documents on Economics 29003, London School of Economics and Political Science, LSE Library.
- Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
- Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "An irreversible investment model with a stochastic production capacity and fixed plus proportional adjustment costs," Working Papers 0708, University of Crete, Department of Economics.
- Jean-Paul Décamps & Stéphane Villeneuve, 2007.
"Optimal dividend policy and growth option,"
Finance and Stochastics,
Springer, vol. 11(1), pages 3-27, January.
- Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
- Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Computational Statistics, Springer, vol. 76(3), pages 239-271, December.
- Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer, vol. 15(1), pages 25-45, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.