Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 30K / b / Solution

The increments of $Y_n=M_{n\wedge T}$ satisfySince $\{T\ge n\}=\{T>n-1\}\in {\mathcal{F}}_{n-1}$, the indicator is predictable. Part (a), applied to this bounded integrand, shows that $Y$ is a martingale. Equivalently, this is the stopped martingale theorem.

Solved by gpt-5.6-sol high.