Equilibrium in economies with incomplete financial markets

Another Proof of the Existence of GEI Equilibrium with Default and Exogenous Collateral

“…To reach our goal, we combine the characterization of asset prices offered by Araújo et al (2005) and the demand approach used by Geanakoplos and Zame (2002). The proof follows lines similar to the usual proof of existence in an exchange economy with complete market structure (see Hildenbrand (1974), or the proof followed by Werner (1985) or Zhang (1996) in the case of incomplete financial markets). The most outstanding feature of our proof is that, even in the presence of real assets, 1 the demand function, having arbitrage-free prices as its domain, satisfies the boundary condition.…”

“…A second answer, proposed initially by Arrow (1953), but more forcefully put forward by Geanakoplos and Polemarchakis (1986), is to express all payoffs in terms of a numeraire good. A third answer, pursued by Cass (1984), Werner (1985), Duffie (1987) and Zhang (1996) is to propose restrictions on asset returns, such as having nominal returns. This paper is organized as follows: in section 2, we describe characteristics of the exogenous collateral model, establish assumptions of the model, and end by stating the notion of equilibrium.…”

“…Therefore, following Werner (1985), in the sequel only the price system (p, π) ∈ N ×△ ++ will be considered.…”

Essays in Dynamic General Equilibrium Theory

“…In two provocative and influential papers, Cass [1,2] showed that the existence of equilibrium could be guaranteed if all the assets promise delivery in fiat money, and he gave an example showing that with such financial assets there could be a multiplicity of equilibrium. Almost simultaneously Werner [9] also gave a proof of existence of equilibrium with financial assets, and Geanakoplos and Polemarchakis [5] showed the same for economies with real assets that promise delivery in the same consumption good. (Geanakoplos [4])…”

A simple method for computing equilibria when asset markets are incomplete

“…Two of them, perhaps most notable of all, are that perfect competition need not necessarily lead to market efficiency, and that nominal assets are in marked contrast to real assets, in terms of their impact on the existence of equilibrium. As regards the latter, equilibria have been shown in Werner (1985) and Cass (2006) to exist when the assets marketed are nominal. But, on the other hand, it has been shown in Hart (1975), by way of example, that, when the assets marketed are real, equilibria may fail to exist for GEI models.…”