Arbitrage Pricing and the Existence of Equilibrium Under Portfolio Constraints
57 Pages Posted: 19 Oct 2003
Date Written: October 2003
Market frictions create portfolios of complicated nature, constrained zero-income portfolios. They generate no income in the future contingencies but matter to risk sharing whether they are mispriced or not. The no arbitrage conditions of the literature may not be qualified for equilibrium conditions in the presence of constrained zero-income portfolios. Thus 'pricing by arbitrage' is far from completely characterizing asset pricing relations. The purpose of this paper is to provide a unified treatment of both asset pricing and equilibrium when asset markets are subject to portfolio constraints. In particular, 'projective arbitrage' is proposed to examine both asset pricing and the existence of equilibrium under portfolio constraints. To formulate the effect of constrained zero-income portfolios on asset pricing and equilibrium, we introduce the local and global laws of one price as an extension of the law of one price to the case with portfolio constraints. The global law of one price is identified as 'pricing by projective arbitrage.' Moreover, the global law of one price provides an important criterion for judging the capability of various notions of arbitrage to characterize equilibrium asset prices under portfolio constraints. The traditional approach to general equilibrium with incomplete markets breaks down in the face of market frictions simply because the law of one price fails.
Keywords: local law of one price, global law of one price, projective arbitrage, equilibrium, portfolio constraints
JEL Classification: G12, D52, C62, G11
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