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

W. Dai and C. C. Heyde

International Journal of Stochastic Analysis, 1996, vol. 9, 1-10

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.

Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/9/541390.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/9/541390.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:541390

DOI: 10.1155/S104895339600038X

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().