Controlling the time discretization bias for the supremum of Brownian Motion

Krzysztof Bisewski, Daan Crommelin, Michel Mandjes

We consider the bias arising from time discretization when estimating the threshold crossing probability $w(b):=\mathbb{P}({\sup }_{t\in [0,1]}{B}_t>b)$, with $(B_t{)}_{t\in [0,1]}$ a…