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zurück | neue Suche | drucken Schachermayer, Walter: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science", Nr. 87, February 27, 2002 SFB Adaptive Information Systems and Modelling in Economics and Management Science Wien, Wirtschaftsuniv., 2002 Daten im WU Online-Katalog | Nutzungsstatistik | Dokument ID: oai:epub.wu-wien.ac.at:epub-wu-01_238 Volltext Download 30 Seiten/308 kB © Urheberrechtshinweis Sie wollen einen permanenten Link direkt zu diesem Dokument, um ihn z.B. auf Ihrer Webseite zu platzieren? Benutzen Sie: http://epub.wu-wien.ac.at/dyn/openURL?id=oai:epub.wu-wien.ac.at:epub-wu-01_238  Abstract: 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)  Schlagworte: Devisenmarkt / Capital-asset-pricing-Modell / Transaktionskosten / Arbitrage / arbitrage / proportional transaction costs / foreign exchange markets / fundamental theorem of asset pricing  Klassifikation: JEL: G10 / G12 / G13 © 2009 Universitätsbibliothek, WU | Technologie und Infrastruktur: Inst. f. Informationswirtschaft | Erstellt für Sie am: 2.9.2010