Let (d S_{t}=left(mu d t+sigma d B_{t} ight)) and (r=0). Is the portfolio (widehat{pi}(t, 1)) self-financing? If

Let \(d S_{t}=\left(\mu d t+\sigma d B_{t}\right)\) and \(r=0\). Is the portfolio \(\widehat{\pi}(t, 1)\) self-financing? If not, find \(\pi^{0}\) such that \(\left(\pi_{t}^{0}, 1\right)\) is self-financing.