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  • A Note on Asymptotic Exponential Arbitrage with Exponentially Decaying Failure Probability

  • Part of
  • Kai Du, Ariel David Neufeld
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 3 / September 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 801-809
    Print publication:
    September 2013
    • Article
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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.