The Duration of Optimal Stopping Problems

Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This research note surveys several variants of optimal stopping problems, extends earlier results in various directions, and shows how many interviews are expected to be conducted in various settings. The focus is on problems that require a decision-maker to choose a candidate from a pool of sequential applicants with no recall, in the vein of previously studied Cayley-Moser, Secretary and Sultan's Dowry problems.