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 d x d matrix-valued stochastic process Sigma_t_t=0^T 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 of Sigma_t_t=0^T. Dually, we interpret a concept used by Kabanov and his co-authors as "strictly consistent price systems". We show that this concept extends the notion of equivalent martingale measures, playing a well-known role in the frictionless case, to the present setting of bid-ask processes Sigma_t_t=0^T. The main theorem states that the bid-ask process Sigma_t_t=0^T satisfies the robust no arbitrage condition if it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Dalang-Morton-Willinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker. An example of a 5-times-5-dimensional process Sigma_t_t=0^2 shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the so-called strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
| Identifer | oai:union.ndltd.org:VIENNA/oai:epub.wu-wien.ac.at:epub-wu-01_238 |
| Date | January 2002 |
| Creators | Schachermayer, Walter |
| Publisher | SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business |
| Source Sets | Wirtschaftsuniversität Wien |
| Language | English |
| Detected Language | English |
| Type | Working Paper, NonPeerReviewed |
| Format | application/pdf |
| Relation | http://epub.wu.ac.at/1512/ |
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