A New Method for Computing Asymptotic Results in Optimal Stopping Problems

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order linear differential equation, makes it possible to systematically obtain these values in many situations. As an example, we address nine variants of the well-known secretary problem, including the classical one, that appear in the literature on the subject, as well as four other unpublished ones.

Automated summary

We propose a new method to compute the asymptotic values of optimal threshold and probability of success in optimal stopping problems. By solving a first-order linear differential equation, these values can be obtained systematically in various situations. We illustrate the method using nine variants of the secretary problem, including both well-known ones from literature and four unpublished ones.