Mixed fractional Brownian motion
Cheridito, Patrick
Bernoulli, Tome 7 (2001) no. 6, p. 913-934 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2001-12-14
Classification:  equivalent measures,  mixed fractional Brownian motion,  semimartingale,  weak semimartingale 
@article{1078951129,
     author = {Cheridito, Patrick},
     title = {Mixed fractional Brownian motion},
     journal = {Bernoulli},
     volume = {7},
     number = {6},
     year = {2001},
     pages = { 913-934},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1078951129}
}

Cheridito, Patrick. Mixed fractional Brownian motion. Bernoulli, Tome 7 (2001) no. 6, pp.  913-934. http://gdmltest.u-ga.fr/item/1078951129/