Abstract
The H-derivative of the expected supremum of fractional Brownian motion {BH(t), t ∈ R+} with drift a ∈ R over time interval [0, T] [Formula: see text] at H = 1 is found. This formula depends on the quantity I , which has a probabilistic form. The numerical value of I is unknown; however, Monte Carlo experiments suggest I ≈ 0.95 . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as H ↑ 1 .