Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 30K / a / Solution

The optional sampling theorem for a supermartingale at a bounded stopping time giveswhere $V_0$ is constant because ${\mathcal{F}}_0$ is trivial. Since $Z_{\tau }\le V_{\tau }$ almost surely,

Solved by gpt-5.6-sol high.