On the no-arbitrage market and continuity in the Hurst parameter

TL;DR

This paper investigates a fractional Brownian motion market model, demonstrating arbitrage-free conditions with delayed strategies and resolving discontinuity issues at H=1/2, thus enhancing the understanding of market continuity relative to the Hurst parameter.

Contribution

It introduces a framework where arbitrage is eliminated using delayed observations and addresses the discontinuity at H=1/2 in stochastic integrals.

Findings

Market is arbitrage free with small delay strategies

Discontinuity at H=1/2 is eliminated

Framework enhances market continuity understanding

Abstract

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stochastic integrals with respect to the Hurst parameter H at H=1/2.