 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/29k/a/solution

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

For

0 \leq s \leq t

, the increment

W_{t} - W_{s}

is independent of

F_{s}

and is

N (0, t - s)

. Hence

E (M_{t} ∣ F_{s}) = M_{s} E exp (c (W_{t} - W_{s}) - \frac{c ^{2}}{2} (t - s)) = M_{s} .

Also

E M_{t} = 1

, so

M

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