Evaluating an Investment Project in an Incomplete Market

Many studies on real options base their arguments upon the assumption that security market is complete to apply the risk-neutral valuation technique. However, when the market is incomplete, in which investment risk is not spanned by existing assets, the investor.s preferences are not risk-neutral, or management is refrained from certain trading strategies, there may exist no unique martingale price of uncertain income streams. In this paper, a dynamic-programming framework for maximizing expected utility of an investor in discrete time is presented to evaluate an investment opportunity in an incomplete market. It is suggested that certainty equivalent (CE) could be applied to value such an investment opportunity. We show that two approaches to certainty equivalent, i.e., the buying price and the selling price approaches, are exactly equal in exponential utility, implying that CE is a fair value for both the buyer and the seller in an incomplete market, subject to the degree of risk aversion. Therefore, the proposed approach, compared to other alternative approaches, is relatively intuitive and easy to apply. With the classic investment problem, it is shown that the option embedded in a project is crucial in decision-making.