I have a question about the following property, which I didn't know so far:
Why does the Itō integral have zero expectation? Is this true for every integrator and integrand? Or is this restricted to special processes, i.e. is $$\mathbb{E}\left[\int f \, \mathrm{d}M\right]=0$$ for all local Martingales $M$ and predictable $f$, such that the integral is well defined?
Thank you for clarification.