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The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time

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"

Identiferoai:union.ndltd.org:VIENNA/oai:epub.wu-wien.ac.at:epub-wu-01_238
Date January 2002
CreatorsSchachermayer, Walter
PublisherSFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business
Source SetsWirtschaftsuniversität Wien
LanguageEnglish
Detected LanguageEnglish
TypeWorking Paper, NonPeerReviewed
Formatapplication/pdf
Relationhttp://epub.wu.ac.at/1512/

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