Self-financing condition
= Self-financing condition
{title2=$dV_t=\phi_t\,dS_t+\psi_t\,dB_t$}
For holdings with value $V_t=\phi_tS_t+\psi_tB_t$, the condition says that all gains and losses arise from the held assets, with no external cash transfer. The stochastic-integrability and admissibility requirements on the holdings are part of a valid trading strategy. Differentiating the value identity alone does not establish self-financing, since changes of holdings can contribute additional terms.