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Investment Timing Under Incomplete Information

GREMAQ-IDEI, Université de Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France, and Europlace Institute of Finance, 39-41 rue Cambon, 75001 Paris, France
GREMAQ-IDEI, Université de Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France, and Department of Economics, London School of Economics and Political Science, WC2A 2AE London, United Kingdom
GREMAQ, Université de Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France
decamps{at}cict.fr
mariotti{at}cict.fr
stephane.villeneuve{at}univ-tlse1.fr

We study the decision of when to invest in a 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 characterized by a continuous and nondecreasing 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 and that the value of the option to invest is not globally increasing with respect to the volatility of the value process.

Key Words: investment under uncertainty; optimal stopping; free boundary; filtering
History: Received: June 10, 2003; revision received: July 5, 2004;

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Comment on "Investment Timing Under Incomplete Information"

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Mathematics of Operations Research 2009 34: 249-254. [Abstract]  

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				M. Klein Comment on "Investment Timing Under Incomplete Information" Mathematics of Operations Research, February 1, 2009; 34(1): 249 - 254. [Abstract] [PDF]

				J.-P. Decamps, T. Mariotti, and S. Villeneuve Investment Timing Under Incomplete Information: Erratum Mathematics of Operations Research, February 1, 2009; 34(1): 255 - 256. [Abstract] [PDF]