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Investment Timing under Incomplete Information

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Author Info
Jean-Paul Decamps
Thomas Mariotti
Stephane Villeneuve
Abstract

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.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Theoretical Economics Paper Series with number 444.

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Date of creation: Jan 2003
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Handle: RePEc:cep:stitep:444

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Keywords: Real options; incomplete information; optimal stopping.;

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  4. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  5. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236. [Downloadable!] (restricted)
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  7. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322. [Downloadable!] (restricted)
  8. 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.
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  9. 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.
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  10. 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. [Downloadable!] (restricted)
  11. Arrow, Kenneth J & Fisher, Anthony C, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," The Quarterly Journal of Economics, MIT Press, vol. 88(2), pages 312-19, May. [Downloadable!] (restricted)
  12. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-90, October. [Downloadable!] (restricted)
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  13. 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 838-68, August. [Downloadable!] (restricted)
  14. Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-12, December. [Downloadable!] (restricted)
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