A note on asymptotic exponential arbitrage with exponentially decaying failure probability

TL;DR

This paper proves that continuous semimartingales satisfying a large deviations estimate enable strong long-term arbitrage opportunities with exponentially decreasing failure probability, extending previous results without requiring diffusion or ergodicity assumptions.

Contribution

It establishes the existence of asymptotic exponential arbitrage with exponentially decaying failure probability for a broader class of semimartingales under large deviations conditions, removing previous restrictions.

Findings

Semimartingales with large deviations estimates admit exponential arbitrage.

No diffusion or ergodicity assumptions are needed.

Provides a quantitative, long-term arbitrage framework.

Abstract

The goal of this paper is to prove a result conjectured in F\"ollmer and Schachermayer [FS07], even in 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 F\"ollmer and Schachermayer [FS07], our result does not assume that S is a diffusion, nor does it need any ergodicity assumption.