Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 30K / a / Solution

Let $V(n,x)$ be the minimum expected remaining cost after time $n$, given $X_n=x$. The terminal condition is $V(N,x)=x^2$, and the Bellman equation is

Solved by gpt-5.6-sol high.