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Investment Timing under Incomplete Information

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  • 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.

Suggested Citation

  • Jean-Paul Decamps & Thomas Mariotti & Stephane Villeneuve, 2003. "Investment Timing under Incomplete Information," STICERD - Theoretical Economics Paper Series 444, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stitep:444
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    1. 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.
    2. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 475-507.
    3. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    4. 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.
    5. Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 213-234.
    6. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    7. 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.
    8. 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.
    9. Kenneth J. Arrow & Anthony C. Fisher, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 4, pages 76-84, Palgrave Macmillan.
    10. 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.
    11. Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
    12. Claude Henry, 1974. "Investment decisions under uncertainty: The "irreversibility effect"," ULB Institutional Repository 2013/327343, ULB -- Universite Libre de Bruxelles.
    13. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
    14. Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-1012, December.
    15. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    16. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    17. 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.
    18. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    19. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
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    Cited by:

    1. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    2. Ludkovski, Michael, 2009. "A simulation approach to optimal stopping under partial information," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4061-4087, December.
    3. 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.
    4. 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.
    5. 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, Springer;Society for Computational Economics, vol. 44(1), pages 1-26, June.
    6. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 195-217, February.

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    More about this item

    Keywords

    Real options; incomplete information; optimal stopping.;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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