Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 29L / 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 $\gamma ={\inf }_{h}E(e^{-hR})$ after rescaling, and the first-order condition preserves exponential form, with $A_n=A_{n+1}/(1+A_{n+1})$.

Solved by gpt-5.6-sol high.