On the fundamental theorem of asset pricing

Abstract

It is well known that existence of equivalent martingale measure (EMM) is essentially equivalent to absence of arbitrage. In this paper, we give an overview of this connection and also include material on this theme from an unpublished article written with Professor Kallianpur. This is included in the book by Kallianpur (7) on Option pricing. In that article, we had introduced a concept of No Approximate Arbitrage with Controlled Risk - NAACR which turns out to be equivalent to the existence of equivalent martingale measure. This seems to be the only result characterising EMM in terms of absence of (suitable notion of) arbitrage in the class simple strategies. Moreover, the proof of this assertion is purely functional analytic, without invoking semimartingales and stochastic integration.