2014/09/01 by Tomomi Matsui, Katsunori Ano · 4 citations
Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #Auction Theory and Applications #Bernoulli trial #Bernoulli's principle #Combinatorics #Computer science #Discrete mathematics #Extension (predicate logic) #Logistic regression #Mathematical analysis #Mathematical optimization #Mathematics #Multiplicative function #Odds #Optimal stopping #Optimization and Search Problems #Optional stopping theorem #Probability theory #Secretary problem #Sequence (biology) #Statistics #Stopping time #Supply Chain and Inventory Management #Upper and lower bounds
paper · pdf · doi:10.1239/jap/1409932681
published in Journal of Applied Probability 51(3), 885-889 (Cambridge University Press)
openalex publication_date 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
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.