= Solution
{c}
The portfolio value is $\Pi_t=\phi_tS_t+\psi_tB_t$. The <self-financing condition> means that changes in holdings are financed by trading within the portfolio, with no external infusion or withdrawal. Thus
$$
\boxed{d\Pi_t=\phi_t\,dS_t+\psi_t\,dB_t
=(\mu\phi_tS_t+r\psi_tB_t)\,dt+\sigma\phi_t\,dW_t.}
$$
The holdings are predictable and satisfy the usual stochastic-integrability and admissibility conditions; without admissibility, doubling strategies would spoil the intended <no-arbitrage> interpretation.
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