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Comment on “Investment timing under incomplete information”. (English) Zbl 1213.60083
Summary: In a recent contribution to this journal, J.-P. Décamps et al. [Math. Oper. Res. 30, No. 2, 472–500 (2005): erratum ibid. 34, No. 1, 255–256 (2009; Zbl 1082.91048)] 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 [loc. cit.] only hold true if the latter outweighs the former.
60G40Stopping times; optimal stopping problems; gambling theory
60G35Signal detection and filtering (stochastic processes)