 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/30l/e/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

E [Y ∣ S_{1}] = E (Y) + cov (Y, S_{1}) V^{- 1} (S_{1} - μ) .

Multiply by

U^{'} (X_{0})

, take expectations, and use part (c):

\frac{E [ U ^{'} ( X _{0} ) S _{1} ]}{E [ U ^{'} ( X _{0} )]} = (1 + r) S_{0} .

Substitution into part (d) gives

π_{0} (Y) = \frac{1}{1 + r} [E (Y) - (μ - (1 + r) S_{0})^{T} V^{- 1} cov (S_{1}, Y)] .

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