Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 3 (2013), 801-809.
A note on asymptotic exponential arbitrage with exponentially decaying failure probability
The goal of this paper is to prove a result conjectured in Föllmer and Schachermayer (2007) in a slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then allows asymptotic exponential arbitrage with exponentially decaying failure probability, which is a strong and quantitative form of long-term arbitrage. In contrast to Föllmer and Schachermayer (2007), our result does not assume that S is a diffusion, nor does it need any ergodicity assumption.
J. Appl. Probab., Volume 50, Number 3 (2013), 801-809.
First available in Project Euclid: 5 September 2013
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Du, Kai; Neufeld, Ariel David. A note on asymptotic exponential arbitrage with exponentially decaying failure probability. J. Appl. Probab. 50 (2013), no. 3, 801--809. doi:10.1239/jap/1378401237. https://projecteuclid.org/euclid.jap/1378401237