The geometry of arbitrage and the existence of competitive equilibrium.
type: Item
instance of: scholarly article
title: The geometry of arbitrage and the existence of competitive equilibrium.
zbMATH Open document ID: 1038.91034
DOI: 10.1016/S0304-4068(02)00074-5
author: Nizar Allouch
author: Cuong Le Van
author: Frank H. jun. Page
published in: Journal of Mathematical Economics
publication date: 2003-04-02T00:00:00Z
review text: In the paper the authors use the basic geometry to shed the light on the relationship between various no-arbitrage conditions founding in the literature. It is shown that if the agents' set of useless not trades are linearly independent, then some well known conditions are equivalent to the strong condition of no-unbounded-arbitrage and, in turn, all are equivalent to the compactness of the set of rational allocations. The problem of the existence of an equilibrium is considered. Shown that under a uniformly condition on preferences weaker then Werner's uniformly condition, the hart-Werner no-arbitrage conditions are sufficient for the existence. With an additional condition of weak no-half-lines it is shown that this conditions are both necessary and sufficient for the existence.
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91B60
zbMATH DE Number: 1891751
zbMATH Keywords: arbitrage
zbMATH Keywords: competitive equilibrium
zbMATH Keywords: recession cones
Wikidata QID: Q57944321
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891751