the question is:
Given are two independent sequences of iid normal random variables $X_i$ and $Y_i$.
Form the ratios $Z_i=X_i/Y_i$.
What is known about the extreme value distribution of the $Z_i$'s, i.e. $\max(Z_1,\ldots,Z_n)$ ? (exclude the trivial case that all have standard normal distributions).
I am looking for a literature reference, since I think somebody must have studied this problem already.