 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-4/28j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Put

b = 1 - R > 0

and

m_{b} = E X_{0}^{b}

U (z_{N}) = U (z_{n}) \prod_{j = n}^{N - 1} X_{j}^{b}

. Thus

E [U (z_{N}) ∣ z_{n}] = U (z_{n}) m_{b}^{N - n} .

As before this is an extended-valued conditional expectation if the required moment is infinite and days remain.

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