Threshold-type Policies for Real Options Using Regime-Switching Models

To investigate the impact of macroeconomic conditions on irreversible investments under a regime switching model, our main effort in this work is to rigorously justify the existence and uniqueness of optimal threshold-type policies. The underlying cash flow process is modeled as a geometric Brownian motion with return rate and volatility depending on a continuous-time Markov chain. The problem is similar to the American style of call options. When dealing either with American options in a financial market or with real options, a common practice in the literature is to postulate threshold-type strategies and to find the optimal threshold levels as solutions of systems of nonlinear algebraic equations. Although from a computational standpoint, this seems to be a reasonable approach, the issue of existence and uniqueness of solutions has never been addressed to date. Instead of assuming the threshold-type policies, this paper establishes that indeed the threshold-type policies are the right choice. Variational inequalities are used to characterize the optimal strategy by an abstract, nonconstructive reasoning. In addition, numerical simulations are also provided to demonstrate quantitative properties and properties of the systems. Copyright © 2012 by SIAM.