Itô's formula with respect to fractional Brownian motion and its application
type: Item
instance of: scholarly article
title: Itô's formula with respect to fractional Brownian motion and its application
zbMATH Open document ID: 0867.60029
DOI: 10.1155/S104895339600038X
author: Juan-Miguel Gracia
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-07-20T00:00:00Z
full work available at URL: https://eudml.org/doc/47673
review text: Summary: 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 \(1/2<H<1\). 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.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 988082
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: Itô's formula
zbMATH Keywords: long range dependence
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Black-Scholes model
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 988082