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

Suggested Citation

Won, Dong Chul and Hahn, Guangsug, Arbitrage Pricing and the Existence of Equilibrium Under Portfolio Constraints (October 2003). Available at SSRN: or

Dong Chul Won (Contact Author)

Ajou University ( email )

College of Business Adminstration
Korea, Republic of (South Korea)

Guangsug Hahn

POSTECH ( email )

San 31, Hoja-dong
Pohang, 790-784
054-279-2031 (Phone)

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