A note on asymptotic exponential arbitrage with exponentially decaying failure probability

2012/07/26 by Du, Kai, Neufeld, Ariel David
#60F10 #60G44 #91G10 #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1207.6281

Abstract

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

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