Lower bound for the expected supremum of fractional Brownian motion using coupling
Abstract
We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index $H\in(0,1)$ over (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for $H\in(0,\tfrac{1}{2})$. Additionally, we derive the PaleyWienerZygmund representation of a Linear Fractional Brownian motion and give an explicit expression for the derivative of the expected supremum at $H=\tfrac{1}{2}$ in the sense of recent work by Bisewski, Dębicki & Rolski (2021).
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.00706
 Bibcode:
 2022arXiv220100706B
 Keywords:

 Mathematics  Probability;
 60G22;
 60G15;
 68M20
 EPrint:
 23 pages, 3 figures