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Investment Timing under Incomplete Information

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  • Décamps, Jean-Paul
  • Mariotti, Thomas
  • Villeneuve, Stéphane

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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Bibliographic Info

Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 115.

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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.
Handle: RePEc:ide:wpaper:661

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  1. 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.
  2. Bergemann, Dirk & Valimaki, Juuso, 2000. "Experimentation in Markets," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 213-34, April.
  3. Godfrey Keller & Sven Rady, 1997. "Optimal Experimentation in a Changing Environment," STICERD - Theoretical Economics Paper Series /1997/333, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Dixit, A., 1988. "Entry And Exit Decisions Under Uncertainty," Papers 91, Princeton, Department of Economics - Financial Research Center.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
  11. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  12. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
  13. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
  14. Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-12, December.
  15. 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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Cited by:
  1. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2003. "Irreversible Investment in Alternative Projects," IDEI Working Papers 193, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jul 2004.
  2. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Society for Computational Economics, vol. 39(2), pages 195-217, February.
  3. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
  4. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Timing Games with Informational Externalities," Levine's Working Paper Archive 122247000000000704, David K. Levine.
  6. Hugonnier, Julien & Morellec, Erwan, 2007. "Corporate control and real investment in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1781-1800, May.
  7. Strebulaev, Ilya A. & Whited, Toni M., 2012. "Dynamic Models and Structural Estimation in Corporate Finance," Foundations and Trends(R) in Finance, now publishers, vol. 6(1–2), pages 1-163, November.
  8. Dandan Song & Zhaojun Yang, 2014. "Utility-Based Pricing, Timing and Hedging of an American Call Option Under an Incomplete Market with Partial Information," Computational Economics, Society for Computational Economics, vol. 44(1), pages 1-26, June.

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