$X_1, X_2, \dots, X_n$ are independently distributed binary random variables. A portfolio is a set of $m < n$ of these.
The value of a portfolio $\{X_{i_1},\dots, X_{i_m}\}$ is $\max(X_{i_1},\dots, X_{i_m})$ (i.e. the first order statistic of the variables in the portfolio).
Is there an efficient algorithm to select from the $n \choose m$ possibilities a portfolio with the highest expected value (i.e. to maximize the expectation of the first order statistic)?
I've only been able to think of the brute force solution to this optimization problem. It doesn't seem that a greedy approach works. Most of what I've been able to find on first order statistics deals with continuous distributions. And all of the work on portfolio choice that I've found deals with maximizing the expected sum.
This article addresses exactly the question I had posted about: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1468-0262.2006.00705.x