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A General Fractional White Noise Theory And Applications To Finance
Author(s) -
Elliott Robert J.,
Van Der Hoek John
Publication year - 2003
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00018
Subject(s) - fractional brownian motion , hurst exponent , white noise , mathematical economics , econometrics , statistical physics , mathematics , brownian noise , brownian motion , economics , noise (video) , computer science , statistics , physics , artificial intelligence , image (mathematics)
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.