= Solution
Let $L=\exp((r-\frac12\sigma^2)(T-t)+\sigma\sqrt{T-t}\,Z)$. Boundedness of $g'$ and integrability of the <lognormal distribution> variable $L$ justify differentiation under the expectation, by dominated convergence:
$$
V_s(t,s)=e^{-r(T-t)}\mathbb E[g'(sL)L].
$$
A differentiable increasing payoff has $g'\geq0$, and $L>0$. Thus the <delta hedge> has
$$
\boxed{\pi_t=e^{-r(T-t)}\mathbb E[g'(S_tL)L]\geq0.}
$$
Moreover $\mathbb EL=e^{r(T-t)}$, so $0\leq\pi_t\leq\|g'\|_\infty$. At maturity the delta is $g'(S_T)\geq0$. The <admissible trading strategy> already constructed therefore uses nonnegative stock holdings throughout replication. After maturity, liquidate the stock position and retain the proceeds in the bank account, so $\pi_t=0$ for $t>T$ if holdings are to be defined for all times.
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