Random variables as pathwise integrals with respect to fractional Brownian motion

Details Random variables as pathwise integrals with respect to fractional Brownian motion Random variables as pathwise integrals with respect to fractional Brownian motion

2011-11-08

arxiv.org/abs/1111.1851v1

Mathematics

Probability

Scientific paper

We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ 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.

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