A SECRETARY PROBLEM WITH GENERAL PAYOFF AND REFUSING

In this paper, we consider a class of seoretary problems with general payoff and the applicants' right to refuse an offer of employment with a certain probability that depends on absolute ranks of applicants and their time of arrival. Under some additional assumption, the optimal stopping rule is derived. In partioular, the optimal stopping rules of maximizing the probability of employing the best applicant and minimizing expected rank are derived respectively.