Evaluating an Investment Project in an Incomplete Market

Many studies on real options base their arguments upon the assumption thatsecurity market is complete to apply the risk-neutral valuation technique. However, whenthe market is incomplete, in which investment risk is not spanned by existing assets, theinvestor s preferences are not risk-neutral, or management is refrained from certain tradingstrategies, there may exist no unique martingale price of uncertain income streams. In thispaper, a dynamic-programming framework for maximizing expected utility of an investor indiscrete 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 investmentopportunity. We show that two approaches to certainty equivalent, i.e., the buying price andthe selling price approaches, are exactly equal in exponential utility, implying that CE is afair value for both the buyer and the seller in an incomplete market, subject to the degree ofrisk aversion. Therefore, the proposed approach, compared to other alternative approaches,is relatively intuitive and easy to apply. With the classic investment problem, it is shownthat the option embedded in a project is crucial in decision-making.