Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura*, Georgiy Shevchenko, Esko Valkeila

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2353-2369
Number of pages17
JournalStochastic Processes and their Applications
Volume123
Issue number6
DOIs
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional Brownian motion Pathwise integral Generalized Lebesgue-Stieltjes integral Arbitrage Replication Divergence integral

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