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Characterization of arbitrage-free markets

Research paper by Eva Strasser

Indexed on: 23 Mar '05Published on: 23 Mar '05Published in: Mathematics - Probability



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.