Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura; Georgiy Shevchenko; Esko Valkeila

doi:10.1016/j.spa.2013.02.015

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arXiv · 1111.1851

Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura·Georgiy Shevchenko·Esko Valkeila

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Abstract

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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Yuliya Mishura, Georgiy Shevchenko, Esko Valkeila. 2012-09-20. Random variables as pathwise integrals with respect to fractional Brownian motion. https://doi.org/10.1016/j.spa.2013.02.015

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