An example of short-term relative arbitrage

TL;DR

This paper demonstrates that in markets with a bounded excess growth rate, relative arbitrage opportunities also exist over very short time intervals under certain conditions.

Contribution

It establishes a link between long-term and short-term relative arbitrage under a time-homogeneity assumption.

Findings

Relative arbitrage exists over arbitrarily short intervals.

Long-term relative arbitrage implies short-term arbitrage under specific conditions.

The paper provides theoretical proof of short-term arbitrage existence.

Abstract

Long-term relative arbitrage exists in markets where the excess growth rate of the market portfolio is bounded away from zero. Here it is shown that under a time-homogeneity hypothesis this condition will also imply the existence of relative arbitrage over arbitrarily short intervals.