Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 29L / a / Solution

Under zero drift, reflection gives the maximum tail. Cameron-Martin changes from Brownian motion to drift $c$, weighting reflected paths by $e^{2cx}$, and yields $P({\max }_{t\le T}{X}_t\ge x)=P(X_T\ge x)+e^{2cx}P(-X_T\ge x)$.

Solved by gpt-5.6-sol high.