A Prophet Inequality Related to the Secretary Problem
This article was first published in Contemporary Mathematics, published by the American Mathematical Society. Copyright © 1992 American Mathematical Society.
NOTE: At the time of publication, the author Theodore Hill was not yet affiliated with Cal Poly.
Let Z1, Z2 , .. . , Zn be independent 0-1-valued random variables. A gambler gels a. reward 1 if he stop8 a.t the time of the last success and otherwise gets no reward. A simple comparison with a Poisson process is used to show that a prophet can do at most e times as well as the gambler using an optimal stopping time. For fixed n, the best constant is (n/(n -l ))"-1.
Theodore P. Hill and Ulrich Krengel. "A Prophet Inequality Related to the Secretary Problem" Contemporary Mathematics 125 (1992): 209-215.
Available at: http://works.bepress.com/tphill/81