Investment under uncertainty: State prices in incomplete markets

An investment's price is the state-price weighted sum of its future payoffs when markets are complete. This is a well established fact in the financial economics field. The investment valuation problem in incomplete markets, however, has attracted the interest of several additional fields, including decision analysis and real options, and has led to a variety of valuation approaches. The approaches differ in their treatment of the investor's existing portfolio, market opportunities to hedge risks, the ability to re-optimize after adding a new investment to one's portfolio, and the investment's divisibility.; This research develops a single valuation approach that produces results consistent with financial economics when markets are complete but is also applicable when the investment is not divisible and the decision maker can only borrow and lend at the risk-free discount rate (markets are incomplete). Results suggest that, given a time- and state-separable utility function, a decision maker's buying price for an investment is approximately equal to the state-price weighted sum of its future payoffs (see Theorems 2.2 and 3.2); results are exact when markets are complete or the utility function is exponential. State prices in incomplete markets have a similar definition as state prices in complete markets in that they are approximately marginal utility based prices. The approach may have computational advantages because the prices can be estimated without solving a full utility maximization problem for each new investment that is evaluated.; The most important application of this work will be in the evaluation of projects that are indivisible and have managerial flexibility in markets that are incomplete (i.e., an important category of real option problems). A comprehensive example of an electrical utility's use of distributed generation to provide system capacity (rather than the typical approach of upgrading transmission and distribution facilities) illustrates how to apply the method. The example shows that the correlation between a new project's payoffs and the existing portfolio has a large effect on the investment decision.