Density estimates for the exponential functionals of fractional Brownian motion

TL;DR

This paper studies the probability density of the exponential functional of fractional Brownian motion, providing a log-normal upper bound using Malliavin calculus techniques.

Contribution

It introduces a novel upper bound for the density of exponential functionals of fractional Brownian motion employing Malliavin calculus.

Findings

Established a log-normal upper bound for the density

Applied Malliavin calculus to fractional Brownian motion

Enhanced understanding of the distributional properties of exponential functionals

Abstract

In this note, we investigate the density of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin's calculus, we provide a log-normal upper bound for the density.