Article2009

No Arbitrage without Semimartingales

Robert A. Jarrow · Philip E. Protter · Hasanjan Sayit

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

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.

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References

1999Continuous Martingales and Brownian Motion 2005Stochastic Integration and Differential Equations 1991Long-Term Memory in Stock Market Prices 2008A General Version of the Fundamental Theorem of Asset Pricing (1994)1994A general version of the fundamental theorem of asset pricing 1989Long-term Memory in Stock Market Prices 1998The fundamental theorem of asset pricing for unbounded stochastic processes 2003Time-changed Lévy processes and option pricing

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