= Solution
For $0\leq t\leq1$, <concavity> of $U$ implies
$$
\begin{aligned}
G(ts_1+(1-t)s_2)
&=\mathbb E\left[U\left(t(m+s_1Z)+(1-t)(m+s_2Z)\right)\right]\\
&\geq tG(s_1)+(1-t)G(s_2),
\end{aligned}
$$
so $G$ is concave.
Since $\mathbb E Z=0$, <Jensen inequality> gives
$$
G(s)=\mathbb E[U(m+sZ)]
\leq U(m+s\mathbb EZ)=U(m)=G(0).
$$
If $0\leq s<t$, concavity and $s=(1-s/t)0+(s/t)t$ yield
$$
G(s)\geq\left(1-\frac st\right)G(0)+\frac stG(t)\geq G(t).
$$
\b[Hence $G$ is decreasing on $[0,\infty)$; this is <scaled centered risk under concave utility>.]
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