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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


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
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DOI: 10.1155/S104895339600038X

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