Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura, Georgiy Shevchenko and Esko Valkeila

Stochastic Processes and their Applications, 2013, vol. 123, issue 6, 2353-2369

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.

Keywords: Fractional Brownian motion; Pathwise integral; Generalized Lebesgue–Stieltjes integral; Arbitrage; Replication; Divergence integral (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:6:p:2353-2369

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DOI: 10.1016/j.spa.2013.02.015

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