Problems of stochastic analysis of Wiener integrals constructed by fractional Brownian motion (Q2755318)
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scientific article; zbMATH DE number 1669783
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Problems of stochastic analysis of Wiener integrals constructed by fractional Brownian motion |
scientific article; zbMATH DE number 1669783 |
Statements
8 November 2001
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fractional integral
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differentiability
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fractional Brownian motion
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\((B,S)\)-market
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Problems of stochastic analysis of Wiener integrals constructed by fractional Brownian motion (English)
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Three problems are considered. In the first problem conditions for the mean-square differentiability and the path differentiability of a fractional integral with kernel that is constructed by a fractional Brownian motion (FBM) are obtained. In the second problem the upper and the lower bounds for the moments of the Wiener integral determined by FBM are established. In the third problem the absence of the equivalent martingale measure for a fractional model of the \((B,S)\)-market is proved and the self-financing portfolio that allows the arbitrage opportunity on this \((B,S)\)-market is constructed.
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