Pretty challenging...

$\displaystyle Q(\lambda)=E_{Q}\{1_{\lambda}\}=E_{P}\{Z1_{\lambda }\}\mbox{ with }0 < Z < \inf$

Suppose that under such a new probability $\displaystyle Q$, the process $\displaystyle B_{t}+\int_{0}^{t}\alpha_{s}ds$ is a Brownian motion; what should $\displaystyle \alpha$ be in order for $\displaystyle Q$ to be a risk neutral measure