  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.
