Abstract
This paper presents a unified approach to valuing investment projects under uncertainty, based on stochastic discount factors, by linking optimal stopping theory to the no-arbitrage principle in asset pricing. An investment threshold for the case where the discount factor and the project’s cash-flow both follow a geometric Brownian motion is derived. Comparative statics of the investment trigger are obtained adding to and clarifying on the uncertainty–investment debate. Finally, two different ways to obtain discount factors are illustrated: spanning assets and representative agent analysis. The link between the characteristics of these different approaches and the optimal investment policy is clarified.
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Helpful comments from Sebastian Gryglewicz, Kuno Huisman, Peter Kort, Magdalena Trojanowska, and an anonymous referee are much appreciated. Part of this research was carried out when the author was at the Department of Mathematics, University of York, Heslington, UK. Funding from the Irish Research Council for the Humanities and Social Sciences (IRCHSS) is gratefully acknowledged.
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Thijssen, J.J.J. Irreversible investment and discounting: an arbitrage pricing approach. Ann Finance 6, 295–315 (2010). https://doi.org/10.1007/s10436-008-0108-4
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DOI: https://doi.org/10.1007/s10436-008-0108-4