In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$ values in total. The objective is to maximize the expected sum of accepted values. We study the performance of static threshold policies, which accept the first $k$ values exceeding a fixed threshold (or all such values, if fewer than $k$ exist). We show that using an optimal threshold guarantees a $γ_k = 1 - e
Tight Guarantees for Static Threshold Policies in the Prophet Secretary Problem