Random variables as pathwise integrals with respect to fractional Brownian motion |
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| Authors: | Yuliya Mishura Georgiy Shevchenko Esko Valkeila |
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| Institution: | 1. Department of Mechanics and Mathematics, Kiev National Taras Shevchenko University, Volodomirska 60, 01601 Kiev, Ukraine;2. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland |
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| Abstract: | 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. |
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| Keywords: | 60G22 60H05 60G15 91G10 |
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