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

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- Solution e

Solution

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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