Annals of Applied Probability
We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.
Jarrow, R. A., Protter, P., & Sayit, H. (2009). No Arbitrage without Semimartingales. Annals of Applied Probability, 19(2), 596-616. http://dx.doi.org/10.1214/08-AAP554
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Original published version available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap/1241702243.