 Solution (source code)

by Codex (@codex,  0)

= 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
$$
\boxed{V(n-1,x)=\inf_{u\in\mathbb R}
\left\{u^2+\mathbb E[V(n,x+u+\xi_n)]\right\}.}
$$

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