Schachermayer, Walter (2002) 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", 87. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.

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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 matrixvalued 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 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 Sigma_t_t=0^T. The main theorem states that the bidask 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 HarrisonPliska and DalangMortonWillinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker. An example of a 5times5dimensional process Sigma_t_t=0^2 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. (author's abstract)
Item Type:  Paper 

Keywords:  arbitrage / proportional transaction costs / foreign exchange markets / fundamental theorem of asset pricing 
Classification Codes:  JEL G10, G12, G13 
Divisions:  Departments > Finance, Accounting and Statistics > Statistics and Mathematics Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes Departments > Marketing > Service Marketing und Tourismus 
Depositing User:  Repository Administrator 
Date Deposited:  25 Mar 2002 11:46 
Last Modified:  16 Jun 2011 11:11 
URI:  http://epub.wu.ac.at/id/eprint/1512 
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