Hey Nate I have a doubt regarding the application of Fubini's theorem in the last step of your calculations. Don't we need to have finiteness of the integral in order to change the order of the iterated integrals? Shouldn't it be Tonelli's lemma?

+1 Thank you very much for the answer, this approach at least at first sight seems more clear to me, anyway as I told Iosif in the comments I'll need some time to go through all the calculations in order to see which one to accept! Thanks again!

+1 Very interesting approach, I'm kinda new in this area a so I will need some time to go through all steps in order to accept one answer or the other! Nonetheless thank you very much!

pretty old question, but still, isn't there a missing square in the last line? The stochastic integral should be squared inside the expectation sign.