# Self-financing portfolio under $Q$-dynamics

I know what given stocks $S_1, ..., S_N$ with SDE's, a portfolio must have a particular value dynamics shape (which depends on the dynamics of $S_1,...,S_N$), if that portfolio is to be self-financing.

However, does this have to hold under every probability measure? Usually we are given dynamics of stocks in P-world, but we also later study the martingale measure $Q$, and we know that the stocks have some known $Q$-dynamics as well.

So, given a portfolio, do the same restrictions on its value dynamics apply in $Q$-world?

$$V_t = \sum_{i=1}^N \phi_i(t) S_{t,i}$$
$$dV_t = \sum_{i=1}^N \phi_i(t) dS_{t,i}$$
Whether these price changes $dS_{t,i}$ are described under this or that probability measures does not matter.