Question: Let $W_t$ be a standard brownian motion under P with filtration $\mathscr F_t$. Let: $$ M_t=\mathbb E[W_T^2|\mathscr F_t] $$ Show that $M$ is a P martingale.
This is simple enough using Tower's law, however, the second part of the question asks:
What is the martingale representation for M. That is, find the previsible process $\phi_t$ with: $$ dM_t=\phi_tdW_t $$ I know that by the martingale representation theorem, the process exists, but how do I go about actually finding it?