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Finitely additive probabilities and the fundamental theorem of asset pricing

Kardaras, Constantinos (2010) Finitely additive probabilities and the fundamental theorem of asset pricing. In: Chiarella, Carl and Novikov, Alexander, (eds.) Contemporary Quantitative Finance. Springer-Verlag Berlin Heidelberg, Berlin, Germany, pp. 19-34. ISBN 9783642034787

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Identification Number: 10.1007/978-3-642-03479-4_2

Abstract

This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that the absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become “local martingales”. The aforementioned result is then used to obtain an independent proof of the classical FTAP, as it appears in Delbaen and Schachermayer (Math. Ann. 300:463–520, 1994). Finally, an elementary and short treatment of the previous discussion is presented for the case of continuous-path semimartingale asset-price processes.

Item Type: Book Section
Official URL: http://www.springer.com/
Additional Information: © 2010 Springer-Verlag Berlin Heidelberg
Divisions: Statistics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 04 Dec 2017 10:28
Last Modified: 26 Jul 2020 23:44
URI: http://eprints.lse.ac.uk/id/eprint/85935

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