The trap of complacency in predicting the maximum

J. du Toit, G. Peskir

Given a standard Brownian motion $B^{\mu }=(B_t^{\mu }{)}_{0\le t\le T}$ with drift $\mu \in \mathbb{R}$ and letting $S_t^{\mu }={\max }_{0\le s\le t}{B}_s^{\mu }$ for $0\le t\le T$, we consider the optimal pre…