Journal article

Random Variables As Pathwise Integrals With Respect To Fractional Brownian Motion

Year:

2013

Published in:

Stochastic Processes and their Applications
Fractional Brownian motion
Pathwise integral
Generalized Lebesgue–Stieltjes integral
Arbitrage
Replication
Divergence integral

We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black–Scholes model of financial market.

Other publications by

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2011
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Real Harmonizable Multifractional Stable Process And Its Local Properties

Publisher: Stochastic Processes and their Applications

Authors: Georgiy Shevchenko, Marco Dozzi, Yulia Mishura, Kostiantyn Ral’chenko

2014
Working paper

Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2007
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Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

2018
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Existence And Uniqueness Of Mild Solution To Stochastic Heat Equation With White And Fractional Noises

Publisher: arxiv

Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura

2022
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Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva

2008
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The Rate Of Convergence For Euler Approximations Of Solutions Of Stochastic Differential Equations Driven By Fractional Brownian Motion

Publisher: Stochastics

Authors: Georgiy Shevchenko, Yulia Mishura

2015
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Asymptotic Behavior Of Mixed Power Variations And Statistical Estimation In Mixed Models

Publisher: Statistical Inference for Stochastic Processes

Authors: Georgiy Shevchenko, Yulia Mishura, Marco Dozzi

2011
Journal article

Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion

Publisher: Random Operators and Stochastic Equations

Authors: Georgiy Shevchenko, Yulia Mishura

2013
Journal article

Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations

Publisher: Statistics & Probability Letters

Authors: Georgiy Shevchenko, Taras Shalaiko

2016
Journal article

Stochastic Wave Equation In A Plane Driven By Spatial Stable Noise

Publisher: Modern Stochastics: Theory and Applications

Authors: Georgiy Shevchenko, Larysa Pryhara