Show that for any $\lambda \in \Re$, the process $Y_{\lambda,t}$ defined as:
$$Y_{\lambda,t} = (S_t/S_0)^\lambda e^{-(r\lambda-\lambda(1-\lambda)\sigma^2/2)t}$$
is a martingale under the risk neutral measure $Q$.
I was thinking that I could apply Ito's Lemma, in which to show that the $\text{d}t$ term will be zero. However, after doing the partial derivatives, the terms do not cancel each other out.
Would really appreciate all the help I can get!