On irreversible investment
AbstractThis paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. It is demonstrated that the marginal profit is indeed equal to the user cost of capital in free intervals where investment occurs in an absolutely continuous way at strictly positive rates. However, the equality is maintained only in expectation on average in blocked intervals where no investment occurs. Whenever the uncertainty is generated by a diffusion, the investment is singular with respect to Lebesgue measure. In contrast to the deterministic and Brownian motion case where lump sum investment takes place only at time zero, the firm responses in general more frequently in jumps to shocks. Nevertheless, lump sum investments are shown to be possible only at information surprises which is defined as unpredictable stopping time or unanticipated information jump even at the predictable time. Furthermore, general monotone comparative statics results are derived for the relevant ingredients of the model. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb--Douglas type and an exponential Levy process modelled economic shock.
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.
Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 15 (2011)
Issue (Month): 4 (December)
Contact details of provider:
Web page: http://www.springerlink.com/content/101164/
Other versions of this item:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- E22 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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.:
- Xin Guo & Jianjun Miao & Erwan Morellec, 2002.
"Irreversible Investment with Regime Shifts,"
FAME Research Paper Series
rp99, International Center for Financial Asset Management and Engineering.
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Robert S. Pindyck, 1986.
"Irreversible Investment, Capacity Choice, and the Value of the Firm,"
NBER Working Papers
1980, National Bureau of Economic Research, Inc.
- Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-85, December.
- Pindyck, Robert S., 1986. "Irreversible investment, capacity choice, and the value of the firm," Working papers 1802-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
- Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
- McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
- Abel, Andrew B. & Eberly, Janice C., 1997. "An exact solution for the investment and value of a firm facing uncertainty, adjustment costs, and irreversibility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 831-852, May.
- Peter Bank & Frank Riedel, 1999.
"Optimal Consumption Choice under Uncertainty with Intertemporal Substitution,"
GE, Growth, Math methods
- Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
- Andrew B. Abel & Janice C. Eberly, 1995.
"The Effects of Irreversibility and Uncertainty on Capital Accumulation,"
NBER Working Papers
5363, National Bureau of Economic Research, Inc.
- Abel, Andrew B. & Eberly, Janice C., 1999. "The effects of irreversibility and uncertainty on capital accumulation," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 339-377, December.
- Andrew B. Abel & Janice B. Eberly, . "The Effects of Irreversibility and Uncertainty on Capital Accumulation," Rodney L. White Center for Financial Research Working Papers 21-95, Wharton School Rodney L. White Center for Financial Research.
- Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
- Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
- repec:wop:humbsf:1999-71 is not listed on IDEAS
- Boyarchenko Svetlana & Levendorskii Sergei Z, 2006.
"General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion,"
The B.E. Journal of Theoretical Economics,
De Gruyter, vol. 6(1), pages 1-51, June.
- Svetlana Boyarchenko & Sergei Levendorskii, 2006. "General option exercise rules, with applications to embedded options and monopolistic expansion," 2006 Meeting Papers 312, Society for Economic Dynamics.
- Svetlana Boyarchenko & Sergei Levendorskii, 2005. "General option exercise rules, with applications to embedded options and monopolistic expansion," Finance 0511001, EconWPA.
- Andrew B. Abel & Janice C. Eberly, 1995.
"Optimal Investment with Costly Reversibility,"
NBER Working Papers
5091, National Bureau of Economic Research, Inc.
- Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-75, March.
- Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
- Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
- Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
- Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- 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.
- Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Working Papers 463, Bielefeld University, Center for Mathematical Economics.
- Giorgio Ferrari & Frank Riedel & Jan-Henrik Steg, 2013.
"Continuous-Time Public Good Contribution under Uncertainty,"
- Giorgio Ferrari & Jan-Henrik Steg & Frank Riedel, 2013. "Continuous-Time Public Good Contribution under Uncertainty," Working Papers 485, Bielefeld University, Center for Mathematical Economics.
- Jan-Henrik Steg, 2012.
"Irreversible investment in oligopoly,"
Finance and Stochastics,
Springer, vol. 16(2), pages 207-224, April.
- Tiziano De Angelis & Giorgio Ferrari, 2013. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Working Papers 477, Bielefeld University, Center for Mathematical Economics.
- Giorgio Ferrari, 2012. "On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems," Papers 1211.0412, arXiv.org, revised Jul 2013.
- Giorgio Ferrari, 2012. "On an Integral Equation for the Free Boundary of Stochastic, Irreversible Investment Problems," Working Papers 471, Bielefeld University, Center for Mathematical Economics.
- 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 Nov 2011.
- Francisco Ruiz-Aliseda & Jianjun Wu, 2007. "Irreversible investment in stochastically cyclical markets," Economics Working Papers 1018, Department of Economics and Business, Universitat Pompeu Fabra.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.