Journal of Applied Probability

A note on asymptotic exponential arbitrage with exponentially decaying failure probability

Kai Du and Ariel David Neufeld

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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.

Article information

J. Appl. Probab., Volume 50, Number 3 (2013), 801-809.

First available in Project Euclid: 5 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91G10: Portfolio theory
Secondary: 60F10: Large deviations 60G44: Martingales with continuous parameter

Asymptotic exponential arbitrage continuous semimartingale model large deviations


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.

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