BFS 2002 

Plenary Address 
Walter Schachermayer
We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a dxd matrixvalued stochastic process specifying the mutual bid and ask prices between d assets.
We introduce the notion of "robust no arbitrage", which is a version of the no arbitrage concept, robust with respect to small changes of the bid ask spreads. Dually, we interpret a concept used by Kabanov and his coauthors as "strictly consistent price systems". We show that this concept extends the notion of equivalent martingale measures, playing a wellknown role in the frictionless case, to the present setting of bidask processes.
The main theorem states that the bidask process satisfies the robust no arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of HarrisonPliska and DalangMortonWillinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker.
An example of a 5x5dimensional process shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the socalled strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker.
http://doob.fam.tuwien.ac.at/~wschach/pubs/