Theoretical Statistics and Mathematics Unit, ISI Delhi

On the Fundamental Theorem of Asset Pricing

by Abhay G. Bhatt and Rajeeva L. Karandikar

It is well known that existence of equivalent
martingale measure (EMM) is {\em essentially}
equivalent to absence of arbitrage. In this paper, we give an overview of this
connection and also include work that we had done with Professor Kallianpur,
which was not published as an article, but is included in the
book by Kallianpur
on Option pricing. This is the 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 characterizing EMM in terms of simple strategies. Moreover, the
proof of this assertion is purely functional analytic, without invoking semimartingales
and stochastic integration.

isid/ms/2015/07 [fulltext]

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