The geometry of arbitrage and the existence of competitive equilibrium.
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.
scientific article; zbMATH DE number 1891751