Random variables as pathwise integrals with respect to fractional Brownian motion
Probability
2013-03-22 v2
Abstract
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.
Cite
@article{arxiv.1111.1851,
title = {Random variables as pathwise integrals with respect to fractional Brownian motion},
author = {Yuliya Mishura and Georgiy Shevchenko and Esko Valkeila},
journal= {arXiv preprint arXiv:1111.1851},
year = {2013}
}