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Type: Journal article
Title: A general fractional white noise theory and applications to finance
Author: Elliott, R.
Van Der Hoek, J.
Citation: Mathematical Finance, 2003; 13(2):301-330
Publisher: Blackwell Publishers
Issue Date: 2003
ISSN: 0960-1627
Statement of
Robert J. Elliott, John Van Der Hoek
Abstract: We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Øksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholes market with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.
Keywords: fractional Brownian motion
fractional white noise
Girasanov's theorem
Clark-Ocone representation theorem
fractional Black-Scholes market
fractional Ito isometry
Description: The definitive version is available at
DOI: 10.1111/1467-9965.00018
Published version:
Appears in Collections:Applied Mathematics publications
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