Characterization of arbitrage-free markets
Abstract
The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, 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 \sigma. The necessity parts of both results are known for the stopping time \sigma=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.
Keywords
Cite
@article{arxiv.math/0503473,
title = {Characterization of arbitrage-free markets},
author = {Eva Strasser},
journal= {arXiv preprint arXiv:math/0503473},
year = {2008}
}
Comments
Published at http://dx.doi.org/10.1214/105051604000000558 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)