International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1996 / Article

Open Access

Volume 9 |Article ID 541390 | 10 pages | https://doi.org/10.1155/S104895339600038X

Itô's formula with respect to fractional Brownian motion and its application

Received01 Jul 1996
Revised01 Oct 1996

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.

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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