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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

Föllmer, H. and Schachermayer, W. (2007). Asymptotic arbitrage and large deviations. Math. Finance Econom. 1, 213–249.CrossRefGoogle Scholar
Jacod, J. and Shiryaev, A. N. (2003). Limit Theorems for Stochastic Processes (Fundamental Principles Math. Sci. 288), 2nd edn. Springer, Berlin.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S. E. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin.Google Scholar
Mbele Bidima, M. L. D. and Rásonyi, M. (2012). {On long-term arbitrage opportunities in Markovian models of financial markets}. Ann. Operat. Res. 200, 131–146.CrossRefGoogle Scholar
Schweizer, M. (1995). On the minimal martingale measure and the Föllmer–Schweizer decomposition. Stoch. Anal. Appl. 13, 573–599.Google Scholar