Risk Aversion, Price Uncertainty, and Irreversible Investments

Abstract

This paper generalizes the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of complete markets. Until now, this theory has only been developed in the cases of risk neutrality or risk aversion in combination with complete markets. Within a general setting, we prove the existence of a unique critical output price that distinguishes price regions in which it is optimal for a risk averse investor to invest and price regions in which one should refrain from investing. We use a class of utility functions that exhibit non-increasing absolute risk aversion to examine the effects of risk aversion, price uncertainty, and other parameters on the optimal investment decision. We find that risk aversion reduces investment, particularly if the investment size is large. Moreover, we find that a rise in price uncertainty increases the value of deferring irreversible investments. This effect is stronger for high levels of risk aversion. In addition, we provide, for the first time, closed-form comparative statics formulas for the risk neutral investor.

Keywords: Investments under uncertainty, real options, risk averse investor, incomplete markets

JEL Classification: C61, D81, G31