We look at a standard no dividends Black-Scholes model and here we have a process Z, which is defined by: Z(t)=(S(t)/H)^p , where H is a positive constant and p=1-2r/sigma^2
I am now asked to show that Z(t)/Z(0) is a positive mean-1 martingale.
My first intuition tells me to use Ito's formula to get dZ(t) and that shouldn't include a dt term, but I somehow keep seeing the dt term when I use Ito. I am getting increasingly frustrated. Can someone help me with this? From there on I would take the expectation and se that E(Z(t))=1.