2022/01/03 by Bisewski, Krzysztof
#60G15 #60G22 #68M20 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2201.00706
We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index H∈(0,1) over (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for H∈(0,\tfrac12). Additionally, we derive the Paley-Wiener-Zygmund representation of a Linear Fractional Brownian motion and give an explicit expression for the derivative of the expected supremum at H=\tfrac12 in the sense of recent work by Bisewski, D\kebicki & Rolski (2021).