A note on asymptotic exponential arbitrage with exponentially decaying failure probability. (English) Zbl 1286.91124

The main result of the paper states that if a price process \(S\) is a continuous semimartingale and satisfies a large deviations estimate (a particular growth condition on the mean-variance tradeoff of \(S\)), then \(S\) allows for asymptotic exponential arbitrage with exponentially decaying failure probability. This statement is a proof of a result conjectured by H. Föllmer and W. Schachermayer [Math. Financ. Econ. 1, No. 3–4, 213–249 (2008; Zbl 1153.91015)], but, in contrast to the latest conjecture, the authors’ result does not assume that \(S\) is a diffusion and does not need any ergodicity assumption.


91G10 Portfolio theory
60F10 Large deviations
60G44 Martingales with continuous parameter
60H30 Applications of stochastic analysis (to PDEs, etc.)


Zbl 1153.91015
Full Text: DOI arXiv Euclid


[1] Föllmer, H. and Schachermayer, W. (2007). Asymptotic arbitrage and large deviations. Math. Finance Econom. 1 , 213-249. · Zbl 1153.91015
[2] Jacod, J. and Shiryaev, A. N. (2003). Limit Theorems for Stochastic Processes (Fundamental Principles Math. Sci. 288 ), 2nd edn. Springer, Berlin. · Zbl 1018.60002
[3] Karatzas, I. and Shreve, S. E. (2000). Brownian Motion and Stochastic Calculus , 2nd edn. Springer, Berlin. · Zbl 0734.60060
[4] 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. · Zbl 1255.90084
[5] Schweizer, M. (1995). On the minimal martingale measure and the Föllmer-Schweizer decomposition. Stoch. Anal. Appl. 13 , 573-599. · Zbl 0837.60042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.