Pretty challenging...

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

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