= Solution
{c}
For $V\in C^{1,2}$, <Itô's formula> gives
$$
dV=\left(V_t+\mu sV_s+\frac{\sigma^2}{2}V_{ss}\right)dt+\sigma V_s\,dW.
$$
Match the Brownian coefficient with the <self-financing portfolio> by choosing the <option delta> $\phi=V_s$ and bond value $\psi B=V-sV_s$. Equating drifts cancels the physical drift $\mu$ and gives
$$
\boxed{V_t+rsV_s+\frac{\sigma^2}{2}V_{ss}-rV=0,
\quad (t,s)\in[0,T)\times\mathbb R,\qquad V(T,s)=F(s).}
$$
This is the <pricing equation for a linear asset with additive noise>. Its spatial <domain> is the whole <real line>, because the asset can be negative. In particular the diffusion term is $\sigma^2V_{ss}/2$, not $\sigma^2s^2V_{ss}/2$. The derivation is <delta hedging> and does not impose a boundary condition at $s=0$.
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