Solution
= Solution
Let $B_t=e^{rt}$ and let $\psi_t$ be the bank-account holding. Then $X_t=\psi_tB_t+\theta_tS_t$. The <self-financing portfolio> condition gives
$$
dX_t=\psi_t\,dB_t+\theta_t\,dS_t
=r(X_t-\theta_tS_t)\,dt+\theta_t\,dS_t.
$$
= Solution
Let $B_t=e^{rt}$ and let $\psi_t$ be the bank-account holding. Then $X_t=\psi_tB_t+\theta_tS_t$. The <self-financing portfolio> condition gives
$$
dX_t=\psi_t\,dB_t+\theta_t\,dS_t
=r(X_t-\theta_tS_t)\,dt+\theta_t\,dS_t.
$$