Equilibria in exchange economies with financial constraints: Beyond the Cass Trick

We consider an exchange economy under incomplete financial markets with purely financial securities and finitely many agents. When portfolios are not constrained, Cass (1984), Duffie (1987) and Florenzano--Gourdel (1992) proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass (1984) in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financial market is constrained by convex restrictions, provided that financial markets are collectively frictionless.