No Arbitrage Under Transaction Costs, with Fractional Brownian Motion and Beyond

Abstract

We establish a simple no-arbitrage criterion that reduces the absence of arbitrage opportunities under proportional transaction costs to the condition that the asset price process may move arbitrarily little over arbitrarily large time intervals.

We show that this criterion is satisfied when the return process is either a strong Markov process with regular points, or a continuous process with full support on the space of continuous functions. In particular, we prove that proportional transaction costs of any positive size eliminate arbitrage opportunities from geometric fractional Brownian motion for H E (0, 1) and with an arbitrary continuous deterministic drift.