Tolerance to arbitrage
The author studies models of a frictionless security market where the prices are continuous processes of bounded \(p\)-variation, \(p\in [1,2)\). Specifically, ``volatility terms'' of the price processes are fractional Brownian motions with index \(1/2<H<1\), \(1/H<p\). An explicit arbitrage trading strategy is constructed for such a market, based on Hardy's inequalities for \(\alpha \)-order power means of the prices. The result is an extension of the already known fact that price processes of bounded variation (\(p=1\)) admit arbitrage.
scientific article; zbMATH DE number 1364494