I would like to get the price of an option which pays at time T the minimum between the logarithm of (S(1,T) / S(1,0)) and the logarithm of (S(2,T) / S(2,0), with the following processes:
(The two brownians motions are not correlated).
I decided to use the martingale approach for this problem. By choosing the risk-less asset as the numeraire, I know I have to use the Radom-Nikodym derivative but I am a little bit stuck. Does anybody have some hints to give regarding this problem?