Stochastic Integration with Respect to Fractional Brownian Motion

Abstract

While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-­similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.