Free lunch for large financial markets with continuous price processes

Abstract

A large financial market is described by a sequence of traditional market models with finite numbers of assets. There are various concepts in the spirit of no asymptotic arbitrage related to the contiguity of a sequence of equivalent martingale measures with respect to the sequence of historical probabilities. In this article, I show that in the case of continuous price processes, the existence of a bicontiguous sequence of martingale measures is equivalent to the property of no asymptotic free lunch with bounded risk.