Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 30L / e / Solution

Fix $A\in {\mathcal{F}}_{n-1}$ and choose the nonnegative predictable strategy with $H_n=1_A$ and all other holdings zero. The assumed inequality yields $E[1_A(X_n-X_{n-1})]\le 0$ for every $A$, equivalent to the supermartingale conditional inequality.