No arbitrage without semimartingales

TL;DR

This paper demonstrates that by restricting trading strategies, arbitrage can be eliminated even in models where price processes are not semimartingales, such as fractional Brownian motion.

Contribution

It introduces a framework allowing non-semimartingale price processes while maintaining no arbitrage through strategy restrictions.

Findings

No arbitrage with fractional Brownian motion under strategy restrictions

Traditional arbitrage possibilities are eliminated in the new setting

Allows for broader classes of price processes in financial modeling

Abstract

We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.