## Geometric Brownian

Hi I just had my exam today morning and I was stuck in the last question and I am dying to find out the answer.

Here the question:

Assume that the process {St} for t>=0 satisfies the GBM as in the black-scholes model, which has a drift rate of r(the risk-free rate) with respect to the risk neutral measure Q. Find lambda not equal 1 such that the process {St^lambda X exp-rt} for t>=0 is a Q-martingale.

Can someone give me a hint on how to solve or help me with it? Thanks.