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Title: On low dimensional case in the fundamental asset pricing theorem with transaction costs
Authors: Grigoriev, P.
First Published: 2005
Citation: Statistics and Decisions, 2005, 23 (1), pp.33-48
Abstract: The well-known Harrison–Plisse theorem claims that in the classical discrete time model of the financial market with finite Ω there is no arbitrage iff there exists an equivalent martingale measure. The famous Dalang–Morton–Willinger theorem extends this result for an arbitrary Ω. Kabanov and Stricker [KS01] generalized the Harrison–Pliska theorem for the case of the market with proportional transaction costs. Nevertheless the corresponding extension of the Kabanov and Stricker result to the case of non-finite Ω fails, the corresponding counter-example with 4 assets was constructed by Schachermayer [S04]. The main result of this paper is that in the special case of 2 assets the Kabanov and Stricker theorem can be extended for an arbitrary Ω. This is quite a surprising result since the corresponding cone of hedgeable claims ÂT is not necessarily closed.
DOI Link: 10.1524/stnd.2005.23.1.33
ISSN: 0721-2631
Type: Article
Appears in Collections:Published Articles, Dept. of Mathematics

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