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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 495–500 | Cite as

Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss

  • Jinfeng LiEmail author
Article

Abstract

Based on a concept of asymptotic exponential arbitrage proposed by Föllmer-Schachermayer, the author introduces a new formulation of asymptotic arbitrage with two main differences from the previous one: Firstly, the realising strategy does not depend on the maturity time while the previous one does, and secondly, the probable maximum loss is allowed to be small constant instead of a decreasing function of time. The main result gives a sufficient condition on stock prices for the existence of such asymptotic arbitrage. As a consequence, she gives a new proof of a conjecture of Föllmer and Schachermayer.

Keywords

Asymptotic arbitrage Time-consistent Small probable maximum loss 

2000 MR Subject Classification

91G10 

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References

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    Dembo, A. and Zeitouni, O., Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998.CrossRefzbMATHGoogle Scholar
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    Du, K. and Neufeld, A. D., A note on asymptotic exponential arbitrage with exponentially decaying failure probability, Journal of Applied Probability, 50(3), 2013, 801–809.MathSciNetCrossRefzbMATHGoogle Scholar
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    Föllmer, H. and Schachermayer, W., Asymptotic arbitrage and large deviations, Mathematics and Financial Economics, 1(3–4), 2008, 213–249.MathSciNetCrossRefzbMATHGoogle Scholar
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    Schweizer, M., On the minimal martingale measure and the Föllmer-Schweizer decomposition, Stochastic Analysis and Applications, 13(5), 1995, 573–599.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.School of ManagementFudan UniversityShanghaiChina

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