Implementing Arrow–debreu Equilibria in Approximately Complete Security Markets

Abstract

This study shows that Arrow-Debreu equilibria in a continuous-time market economy with an infinite-dimensional martingale generator can be implemented in "approximately complete security markets," in which every bond of any maturity is traded and any contingent claim is approximately replicated with any given precision. I introduce "approximate security market equilibrium" as a generalized concept of security market equilibrium. I demonstrate that an Arrow-Debreu equilibrium in the economy can be identified with an approximate security market equilibrium in the approximately complete markets.