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Comment on "Investment Timing Under Incomplete Information"

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In a recent contribution to this journal, Décamps et al. [Décamps, J.-P., T. Mariotti, S. Villeneuve. 2005. Investment timing under incomplete information. Math. Oper. Res. 30(2) 472–500] analyze 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. Using filtering and martingale techniques, they find that (i) the decision maker always benefits from an uncertain drift relative to an average drift situation, and (ii) drift uncertainty unambiguously delays investment. Using the principle of smooth fit, I derive an analytical solution to the problem and give a numerical example that shows that both claims do not hold true in general. My analysis shows that the impact of drift uncertainty on the value of the option to invest and the optimal timing of investment is governed by two separate effects: the impact of uncertainty per se and the impact of learning. In particular, the results of Décamps et al. only hold true if the latter outweighs the former.

Key Words: investment under uncertainty; optimal stopping; free boundary; filtering
History: Received: November 18, 2007; revision received: August 25, 2008;

Related articles in Mathematics of Operations Research:

Investment Timing Under Incomplete Information

Jean-Paul Décamps, Thomas Mariotti, and Stéphane Villeneuve
Mathematics of Operations Research 2005 30: 472-500. [Abstract]