Journal article
Random Variables As Pathwise Integrals With Respect To Fractional Brownian Motion
Year:
2013Published in:
Stochastic Processes and their ApplicationsFractional 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.