Published in Contemporary Mathematics, Volume 125, Issue 1, January 1, 1992, pages 191-207.
This article was first published in Contemporary Mathematics, published by the American Mathematical Society. Copyright © 1992 American Mathematical Society. The original publication is available for purchase at http://ams.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-125.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems, including extensions and variations, descriptions and examples of the main proof techniques, and a list of a number of basic open problems.