Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss

Jinfeng Li

Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 495 -500.

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Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 495 -500. DOI: 10.1007/s11401-019-0147-3
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Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss

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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

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Jinfeng Li. Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss. Chinese Annals of Mathematics, Series B, 2019, 40(4): 495-500 DOI:10.1007/s11401-019-0147-3

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References

[1]

Dembo A, Zeitouni O. Large Deviations Techniques and Applications, 1998, New York: Springer-Verlag

[2]

Du K, Neufeld A D. A note on asymptotic exponential arbitrage with exponentially decaying failure probability. Journal of Applied Probability, 2013, 50(3): 801-809

[3]

Föllmer H, Schachermayer W. Asymptotic arbitrage and large deviations. Mathematics and Financial Economics, 2008, 1(3–4): 213-249

[4]

Schweizer M. On the minimal martingale measure and the Föllmer-Schweizer decomposition. Stochastic Analysis and Applications, 1995, 13(5): 573-599

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