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A Note on Asymptotic Exponential Arbitrage with Exponentially Decaying Failure Probability

Part of: Mathematical finance Limit theorems Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Kai Du  and
Ariel David Neufeld
Kai Du*
Affiliation:
ETH Zürich
Ariel David Neufeld*
Affiliation:
ETH Zürich
*
∗ Postal address: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
∗ Postal address: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
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Abstract

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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.

Keywords

Asymptotic exponential arbitragecontinuous semimartingale modellarge deviations

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 60F10: Large deviations 60G44: Martingales with continuous parameter
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 801 - 809
Copyright
© Applied Probability Trust 

References

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