On the Different Notions of Arbitrage and Existence of Equilibrium

In this paper we first prove an equilibrium existence theorem for finite dimensional economies with unbounded below consumption sets. We only assume that the individually rational utility set is compact and use the demand approach instead of the standard Negishi's approach. We next compare the different concepts of no-arbitrage that have been used in the literature and give conditions for equivalence between absence of arbitrage and existence of equilibrium. Lastly, we introduce the concept of strong unbounded arbitrage and show that the absence of strong unbounded arbitrage implies the compactness of the individually rational utility set.