Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 439-448
doi:10.1155/S104895339600038X
Abstract
Fractional Brownian motion (FBM) with Hurst index 1/2<H<1 is not a
semimartingale. Consequently, the standard Itô calculus is not available for
stochastic integrals with respect to FBM as an integrator if 1/2<H<1. In this
paper we derive a version of Itô's formula for fractional Brownian motion. Then,
as an application, we propose and study a fractional Brownian Scholes stochastic
model which includes the standard Black-Scholes model as a special case and is
able to account for long range dependence in modeling the price of a risky asset.
This article is dedicated to the memory of Roland L. Dobrushin.