Trying to figure out how to solve problems on the 'form':
Find a real number $z$ and a square integrable, adapted process $\psi(s,w)$ such that
$$G(w) = z + \int \psi(s,w)\,dB_s(w)$$
for som process $G(w)$.
In the case I'm working on now I have $G(w) = (B^2_T(w)-T)\exp(B_T(w)-T)$.
So using the Martingale representation theorem I have that:
$$G(w) = E[G] + \int \psi(s,w)\,dB_s(w)$$
and I've already calculated $E[G]$ to be $T^2e^{-T/2}$. So it only remains to show what $\psi(s,w)$ is.
What I've done now is to apply the Itô formula on $G$, as he's done in other old exams, but I can't really understand what he's doing because his handwriting is terrible. But as I said he uses the Itô formula and uses the '$dB_s$'-term as the $\psi(s,w)$ but he's changing it and that step I can't really tell what he is doing. Does anyone know?
From the Itô formula I get $dG(w) = (B_s^2 + 2B_s - 2s)e^{B_s-s}dB_s(w) + (\ldots)dt$
Thanks in advance!