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A note on asymptotic exponential arbitrage with exponentially decaying failure probability

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  • Kai Du
  • Ariel David Neufeld

Abstract

The goal of this paper is to prove a result conjectured in F\"ollmer and Schachermayer [FS07], even in 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 F\"ollmer and Schachermayer [FS07], our result does not assume that S is a diffusion, nor does it need any ergodicity assumption.

Suggested Citation

  • Kai Du & Ariel David Neufeld, 2012. "A note on asymptotic exponential arbitrage with exponentially decaying failure probability," Papers 1207.6281, arXiv.org.
    • Handle: RePEc:arx:papers:1207.6281
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    File URL: http://arxiv.org/pdf/1207.6281
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