 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/30k/b/solution

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

The increments of

Y_{n} = M_{n \land T}

satisfy

Y_{n} - Y_{n - 1} = 1_{{T \geq n}} (M_{n} - M_{n - 1}) .

Since

{T \geq n} = {T > n - 1} \in F_{n - 1}

, the indicator is predictable. Part (a), applied to this bounded integrand, shows that

Y

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