 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/29k/b/solution

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

θ_{n}

shares are held during period

n

, the remaining wealth

X_{n - 1} - θ_{n} S_{n - 1}

is in the bank account. Self-financing therefore gives

X_{n} = θ_{n} S_{n} + (1 + r) (X_{n - 1} - θ_{n} S_{n - 1}),

which rearranges to the required equation.

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