The argument for the generic existence of competitive equilibria when the asset market is incomplete can be formulated with symmetric treatment of all individuals.

This paper analyses the impact of multiple competitive equilibria and complete markets in a simple general equilibrium model. A random selection from the equilibrium correspondence of a finite exchange economy defines probability distributions on equilibrium prices. Asset markets allow traders...

The asset market is incomplete. Fix-price equilibria exist. Price regulation Pareto improves on a competitive allocation.

In an incomplete asset market, firms compute the value of production plans by approximating them with the payoffs of portfolios of marketed assets; equivalently, by projecting their payoffs on the span of the payoffs of marketed assets; equivalently, they apply the capital asset pricing model...

The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals under uncertainty; this is the case even if the asset market is incomplete.

At arbitrary prices of commodities and assets, fix-price equilibria exist under weak assumptions: endowments need not satisfy an interiority condition, utility functions need only satisfy very weak monotonicity requirement, and the asset return matrix allows for redundant assets. Prices of...

In an economy with a non-atomic measure space of assets and exchangeable risks, the Arbitrage Pricing Theory (APT) holds exactly; and factors are structurally specified, which allows for an economic interpretation.