Investment Timing under Incomplete Information
We study the decision of when to invest in an indivisible project whose value is perfectly observable but driven by a parameter that is unknown to the decision maker ex ante. This problem is equivalent to an optimal stopping problem for a bivariate Markov process. Using filtering and martingale techniques, we show that the optimal investment region is characterised by a continuous and non-decreasing boundary in the value/belief state space. This generates path-dependency in the optimal investment strategy. We further show that the decision maker always benefits from an uncertain drift relative to an 'average' drift situation. However, a local study of the investment boundary reveals that the value of the option to invest is not globally increasing with respect to the volatility of the value process.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2000|
|Date of revision:||Apr 2004|
|Publication status:||Published in Mathematics of Operations Research, vol. 30, n°2, mai 2005, p. 472-500.|
|Contact details of provider:|| Postal: Manufacture des Tabacs, Aile Jean-Jacques Laffont, 21 Allée de Brienne, 31000 TOULOUSE|
Phone: +33 (0)5 61 12 85 89
Fax: + 33 (0)5 61 12 86 37
Web page: http://www.idei.fr/
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.:
- Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
- Godfrey Keller & Sven Rady, 1999.
"Optimal Experimentation in a Changing Environment,"
Review of Economic Studies,
Oxford University Press, vol. 66(3), pages 475-507.
- Godfrey Keller & Sven Rady, 1997. "Optimal Experimentation in a Changing Environment," STICERD - Theoretical Economics Paper Series 333, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Godfrey Keller & Sven Rady, 1998. "Optimal Experimentation in a Changing Environment," Game Theory and Information 9801001, EconWPA.
- Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
- Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, March.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-990, October.
- Thomas Sargent, "undated". "Matlab code for Jovanovic's matching model," QM&RBC Codes 24, Quantitative Macroeconomics & Real Business Cycles.
- Dirk Bergemann & Juuso Valimaki, 1997. "Market Diffusion with Two-Sided Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 773-795, Winter.
- Dirk Bergemann & Juuso Valimaki, 1996. "Market Diffusion with Two-Sided Learning," Cowles Foundation Discussion Papers 1138, Cowles Foundation for Research in Economics, Yale University.
- Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
- Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
- Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
- Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 213-234.
- Dirk Bergemann & Juuso Valimaki, 1996. "Experimentation in Markets," Discussion Papers 1220, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Dirk Bergemann & Juuso Valimaki, 1999. "Experimentation in Markets," Cowles Foundation Discussion Papers 1214, Cowles Foundation for Research in Economics, Yale University.
- Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
- Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
- Dixit, A., 1988. "Entry And Exit Decisions Under Uncertainty," Papers 91, Princeton, Department of Economics - Financial Research Center.
- Kenneth J. Arrow & Anthony C. Fisher, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," The Quarterly Journal of Economics, Oxford University Press, vol. 88(2), pages 312-319.
- Felli, Leonardo & Harris, Christopher, 1996. "Learning, Wage Dynamics, and Firm-Specific Human Capital," Journal of Political Economy, University of Chicago Press, vol. 104(4), pages 838-868, August.
- Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
- Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
- Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-1012, December. Full references (including those not matched with items on IDEAS)