A note on asymptotic exponential arbitrage with exponentially decaying failure probability.

• Autores: Kai Du, Ariel David Neufeld
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 3, 2013, págs. 801-809
• Idioma: inglés
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• Resumen

  • 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.