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December 2001 Mixed fractional Brownian motion
Patrick Cheridito
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Bernoulli 7(6): 913-934 (December 2001).

Abstract

We show that the sum of a Brownian motion and a non-trivial multiple of an independent fractional Brownian motion with Hurst parameter H ∈ (0,1] is not a semimartingale if H ∈ (0, ½) ∪ (½, ¾], that it is equivalent to a multiple of Brownian motion if H = ½ and equivalent to Brownian motion if H ∈ ( ¾ , 1]. As an application we discuss the price of a European call option on an asset driven by a linear combination of a Brownian motion and an independent fractional Brownian motion.

Citation

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Patrick Cheridito. "Mixed fractional Brownian motion." Bernoulli 7 (6) 913 - 934, December 2001.

Information

Published: December 2001
First available in Project Euclid: 10 March 2004

zbMATH: 1005.60053
MathSciNet: MR1873835

Keywords: equivalent measures , mixed fractional Brownian motion , Semimartingale , weak semimartingale

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

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Vol.7 • No. 6 • December 2001
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