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Investment Timing under Incomplete Information

  • Jean-Paul Decamps
  • Thomas Mariotti
  • Stephane Villeneuve

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
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Dirk Bergemann & Juuso Valimaki, 1999. "Experimentation in Markets," Cowles Foundation Discussion Papers 1214, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
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  7. 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.
  8. Dirk Bergemann & Juuso Valimaki, 1996. "Market Diffusion with Two-Sided Learning," Cowles Foundation Discussion Papers 1138, Cowles Foundation for Research in Economics, Yale University.
  9. Dixit, A., 1988. "Entry And Exit Decisions Under Uncertainty," Papers 91, Princeton, Department of Economics - Financial Research Center.
  10. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
  11. 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.
  12. Keller, Godfrey & Rady, Sven, 1999. "Optimal Experimentation in a Changing Environment," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 475-507, July.
  13. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
  14. 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.
  15. Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-12, December.
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