Journal of Applied Probability

A note on asymptotic exponential arbitrage with exponentially decaying failure probability

Kai Du and Ariel David Neufeld

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 3 (2013), 801-809.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1378401237

Digital Object Identifier
doi:10.1239/jap/1378401237

Mathematical Reviews number (MathSciNet)
MR3102515

Zentralblatt MATH identifier
1286.91124

Subjects
Primary: 91G10: Portfolio theory
Secondary: 60F10: Large deviations 60G44: Martingales with continuous parameter

Keywords
Asymptotic exponential arbitrage continuous semimartingale model large deviations

Citation

Du, Kai; Neufeld, Ariel David. A note on asymptotic exponential arbitrage with exponentially decaying failure probability. J. Appl. Probab. 50 (2013), no. 3, 801--809. doi:10.1239/jap/1378401237. https://projecteuclid.org/euclid.jap/1378401237


Export citation

References

  • Föllmer, H. and Schachermayer, W. (2007). Asymptotic arbitrage and large deviations. Math. Finance Econom. 1, 213–249.
  • Jacod, J. and Shiryaev, A. N. (2003). Limit Theorems for Stochastic Processes (Fundamental Principles Math. Sci. 288), 2nd edn. Springer, Berlin.
  • Karatzas, I. and Shreve, S. E. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin.
  • 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.
  • Schweizer, M. (1995). On the minimal martingale measure and the Föllmer–Schweizer decomposition. Stoch. Anal. Appl. 13, 573–599.