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

Du, Kai; Neufeld, Ariel David

J. Appl. Probab. 50, No. 3, 801-809 (2013).

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.

Reviewer: Anatoliy Swishchuk (Calgary)

MSC:

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

Keywords:

asymptotic exponential arbitrage; continuous semimartingale model; large deviations

Citations:

Zbl 1153.91015

References:

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