Asymptotic forms for the optimal expected payoffs (minimal costs) for a generalized class of "Secretary" problems are investigated by an analysis of a related family of differential equations. A class of unbounded payoff functions with bounded expected payoffs is determined and methods for generating the expected payoffs are developed.
"On a Class of Secretary Problems." Ann. Probab. 1 (3) 417 - 427, June, 1973. https://doi.org/10.1214/aop/1176996936