Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 29L / c

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- Solution c

Solution

Substitution of

F (n + 1, x) = B_{n + 1} e^{- A_{n + 1} x}

separates the infima over investment and consumption. The investment contributes

γ = in f_{h} E (e^{- h R})

after rescaling, and the first-order condition preserves exponential form, with

A_{n} = A_{n + 1} / (1 + A_{n + 1})

.

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