 Solution

A previsible strategy selects $({\varphi }_n,{\psi }_n)$ using only ${\mathcal{F}}_{n-1}$, before the price changes from time $n-1$ to time $n$ occur. Thus these holdings cannot exploit future information.

The self-financing portfolio condition values both the old and newly rebalanced holdings at the same time-$n$ prices:Their equality says that rebalancing uses only the proceeds of selling existing assets: there is no external deposit or withdrawal. In particular, the changes in holdings have zero net cost at the current prices. The holdings for the following period may use the newly available information in ${\mathcal{F}}_n$.