A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping. (September 2014)

• Record Type: Journal Article
• Authors: Matsui, Tomomi; Ano, Katsunori
• Is Part Of: Journal of applied probability. Volume 51:Number 3(2014)
• Page Start: 885
• Page End: 889
• Publication Date: 2014-09
• Subjects: Optimal stopping, -- odd problem, -- lower bound, -- secretary problem, -- Maclaurin's inequality; 60G40, -- 60L15; 519.2
• DOI: 10.1017/S0021900200011748
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N . This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.