Complete and Incomplete Markets with Short-Sale Constraints

This paper argues that the introduction of a short-sale constraint in the Arrow-Radner frameworkinvalidates standard definitions of complete and incomplete markets. In this constrained set-up,two threshold values with familiar properties arise.The case of a zero short-sale bound set on some security fulfills the standard definition ofincomplete financial markets. Beyond a particular level of the short-sale bound financial marketsare complete, since the short-sale constraint is not active.For intermediate bounds the distinction between complete and incomplete financial markets isblurred. Although some technical definitions hold, agents can not fully transfer wealth amongstates. These intermediate cases, called technically incomplete markets, exhibit interestingwelfare properties. For instance, the resulting equilibrium allocations may not be Pareto dominatedby those of the non-restricted complete markets equilibrium.