# Testing for difference in means for utility of wealth

Assume you have 2 different investment strategies, A and B. You simulate how A and B perform on the same $N$ time series of returns and compute the resulting utility of wealth. $N$ is large, say 100000.

How would you test if the expected utility from investment strategy B is greater than the expected utility from investment strategy A?

I was thinking of using a t-test. Yet, I am not sure whether it should be a standard t-test (we have different strategies) or a paired one (since the return data are the same)? Or should I, since the terminal utilities are not going to be normally distributed, instead choose one of the Wilcoxon tests? If so, again, paired (Wilcoxon signed-rank test) or not paired (Mann-Whitney U test)? Or should I resort to bootstrapping from the different utilities and compare their mean thus?

Side note:
Personally, I am sceptical about the Mann-Whitney U test since it checks if one sample is stochastically greater than the other, not for the difference in means.