We introduce and solve a new class of “downward-recursive” static portfolio choice problems. An individual simultaneously chooses among ranked stochastic options, and each choice is costly. In the motivational application, just one may be exercised from those that succeed. This often emerges in practice, such as when a student applies to many colleges.
We show that a greedy algorithm finds the optimal set. The optimal choices are “less aggressive” than the sequentially optimal ones, but “more aggressive” than the best singletons. The optimal set in general contains gaps. We provide a comparative static on the chosen set.
Keywords: College application, Submodular optimization, Greedy algorithm, Directed search