Arbitrage and Valuation with a Minimum Wealth Constraint

Chong Min Kim
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Chong Min Kim: Kookmin University

Korean Economic Review, 1997, vol. 13, issue 1, 37-47

Abstract: This purpose of this paper is to study the relation among “absence of arbitrage†, “viability of a price pair†, and “existence of a linear pricing rule†in many interesting spaces with a minimum wealth constraint imposed on consumption sets. The study of a relation among these concepts takes roots in Kreps, which provides a rationale of asset pricing theories based on pricing rules by arbitrage. The main contribution of this paper is to establish the equivalence relation with a minimum wealth constraint imposed on a consumption set. Inspired by Mas-Colell, we consider investors with uniformly proper preferences. We generalize the equivalence relation to economies where investors trade contingent claims in markets with transaction costs.

Date: 1997
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