Corporate investment in an economy without a complete set of contingent claims markets has the characteristic of a public good in the sense that the stockholders’ consumption planscannot be separated from, but depend on, the specific investment plans of the firms. Drèze [4] has shown that a constrained Pareto optimal (CPO) allocation of investment in a stock market economy must satisfy a generalization of the Samuelson [24] condition for efficient production of public goods: the investment plan should maximize a weighted sum of the stockholders’ personal valuations of future output minus current input cost. However, except for those special cases in which CPO investment plans are unanimously supported by stockholders (see [17], [20], and [2]), the theory of the firm in incomplete markets lacks a suitable maximization criterion. Although the Drèze-Samuelson condition is a most appealing candidate, it is not unanimously preferred by stockholders, each of whom prefers that his or her own valuation of future output receives all the weight in the investment decision. Furthermore, the application of the Drèze-Samuelson condition depends on the correct revelation of stockholders’ preferences, which, in the absence of special inducements, cannot be expected from economic agents.

Single-period portfolio selection deals with the allocation of an investor's initial wealth to a finite number of risky assets according to his preferences over random final wealth. The purpose of this paper is to study chance-constrained portfolio selection from the point of view of utility theory.