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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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Suggested Citation

  • Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
  • Handle: RePEc:ide:wpaper:661
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    References listed on IDEAS

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    Citations

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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.

    More about this item

    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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