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February 2005 Characterization of arbitrage-free markets
Eva Strasser
Ann. Appl. Probab. 15(1A): 116-124 (February 2005). DOI: 10.1214/105051604000000558

Abstract

The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem 2.1, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906–925] from diffusion processes to arbitrary continuous semimartingales. The second main result, Theorem 2.4, is a characterization of a weaker notion of no-arbitrage in terms of the existence of supermartingale densities. The pertaining weaker notion of no-arbitrage is equivalent to the absence of immediate arbitrage opportunities, a concept introduced by Delbaen and Schachermayer [Ann. Appl. Probab. 5 (1995) 926–945].

Both results are stated in terms of conditions for any semimartingales starting at arbitrary stopping times σ. The necessity parts of both results are known for the stopping time σ=0 from Delbaen and Schachermayer [Ann. Appl. Probab. 5 (1995) 926–945]. The contribution of the present paper is the proofs of the corresponding sufficiency parts.

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Eva Strasser. "Characterization of arbitrage-free markets." Ann. Appl. Probab. 15 (1A) 116 - 124, February 2005. https://doi.org/10.1214/105051604000000558

Information

Published: February 2005
First available in Project Euclid: 28 January 2005

zbMATH: 1071.60061
MathSciNet: MR2115038
Digital Object Identifier: 10.1214/105051604000000558

Subjects:
Primary: 60H05
Secondary: 90A09

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.15 • No. 1A • February 2005
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