I try to be as concise as possible. Basically I'm following the text "Arbitrage Theory in Continuous Time", by Tomas Bjork.
I put here the point where I'm stuck: Chapter 6 - Portfolio Dynamics.
Where does Equation n. 6.7 come from? I mean, the author probably applies the Ito formula to some function, but actually there are no generalized Ito processes in the discussion in order to justify it.