Heads-up this forms part of an assignment question so I'm really just looking for a foothold on how to go about solving it.

Given two standard Brownian Motions such that

Find the MGF:

My thoughts...

I know the distribution for Bt & Ws, so my first thought is to at least define the double integral (based on the joint pdf for a bivariate normal distribution, given I know the mean/var for both the Bt & Ws processes, as well as their correlation coeff.). I can then try to solve that

Is there an alternate/more-sane approach? Perhaps involving application of Ito's Lemma/stoch.calc rules?

Help gratefully received