Irreversible investment with Cox–Ingersoll–Ross type mean reversion

Abstract

We solve a Dixit and Pindyck type irreversible investment problem in continuous time under the assumption that the project value follows a Cox–Ingersoll–Ross process. This setup works well for modeling foreign direct investment in the framework of real options, when the exchange rate is uncertain and the project value fixed in a foreign currency. We indicate how the solution qualitatively differs from the two classical cases: geometric Brownian motion and geometric mean reversion. Furthermore, we discuss analytical properties of the Cox–Ingersoll–Ross process and demonstrate potential advantages of this process as a model for the project value with regard to the classical ones.