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 [31] setting; agents may trade claims continuously 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 economy which has only a finite number of securities.This is done by opening the "right" set of securities markets, a set which effectively completes markets for the continuous trading Radner economy.