Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-Lived Securities

A two-period (0 and T) Arrow-Debreu economy is set up with a general model of uncertainty. We suppose that an equilibrium exists for this economy. The Arrow-Debreu economy is placed in a Radner (dynamic) setting; agents may trade claims at any time during [0,T]. Under appropriate conditions it is possible to implement the original Arrow-Debreu equilibrium, which may have an infinite-dimensional commodity space, in a Radner equilibrium with only a finite number of securities. This is done by opening the “right” set of security markets, a set which effectively completes markets for the Radner economy.