Journal article

Random Variables As Pathwise Integrals With Respect To Fractional Brownian Motion

Year:

2013

Published in:

Stochastic Processes and their Applications

Authors:

, ,

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.

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