 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/30l/e/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Fix

A \in 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})] \leq 0

for every

A

, equivalent to the supermartingale conditional inequality.

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