Complete and Incomplete Markets with Short-Sale Constraints

This paper argues that the introduction of a short-sale constraint in the ArrowRadner framework invalidates 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 of “incomplete” financial markets. Beyond a particular level of the short-sale bound financial markets are “complete”, since the short-sale constraint is not active. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto dominated by those of the non-restricted complete markets equilibrium.