Investment Timing Under Incomplete Information

Abstract

* We are grateful to Bruno Biais, Nicole El Karouni, Christian Gollier and Damien Lamberton for thoughtful discussions and suggestions. We would also like to thank seminar participants at ESC Toulouse, Institut Henri Poincaré and Séminaire Bachelier for their comments. Financial support from STICERD is gratefully acknowledged by the second author. We remain, of course, solely responsible for the content of this paper. AbstractWe 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.

Acquisition of Project-Specific Assets with Bayesian Updating

“…(a) We closely follow the proof of Proposition 7.1 in Decamps et al (2005). Upon inspection of the objective function R τ (·), it is clear that the optimal policy, if it exists, should be stationary because the discounted reward function e −αt g(p) is homogeneous in time.…”

“…Employing the methods of stochastic analysis, they obtained an optimal policy which is stationary and characterized by a threshold on the posterior probability. Decamps et al (2005) also employed Shiryaev's framework to study the optimal time to invest in an asset with an unknown underlying value. In their model, the reward from stopping is the Brownian motion itself rather than the expected value of the time-integral of a Brownian motion.…”

Evaluation of firm’s loss due to incomplete information in real investment decision

“…Hsu and Lambrecht (2003) introduce asymmetric and incomplete information in real options in the context of a patent race. Using the filtering theory, Bernardo and Chowdhry (2002) and Décamps, Mariotti, and Villeneuve (2005) have investigated models in which a firm has incomplete information about parameters of its own profit flow rather than the competitors' behavior. Furthermore, Grenadier and Wang (2005) and Nishihara and Shibata (2007) have examined the effect of asymmetric information between the owner and the manager in the single firm.…”

Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach

“…For example, optimal liquidation problems with an unknown drift were studied in [19] and [20], and with an unknown jump intensity in [35]. In the context of American-style option valuation, the effect of incomplete information on optimal exercise was also considered in [16], [25] and [43]. All of the above examples consider incomplete information about the parameters of a time-homogenous process.…”