Lower Bounds for Bruss’ Odds Problem with Multiple Stoppings

Published Online:https://doi.org/10.1287/moor.2015.0748

References

  • Ano K (2001) Multiple selection problem and OLA stopping rule. Sci. Math. Japon 53(2):335–346.Google Scholar
  • Ano K, Kakie N, Miyoshi N (2011) Odds theorem in Markov-dependent trials with multiple selection chances. RIMS Kokyuroku, Kyoto University 1734:212–219.Google Scholar
  • Ano K, Kakinuma H, Miyoshi N (2010) Odds theorem with multiple selection chances. J. Appl. Probab. 47(4):1093–1104.CrossrefGoogle Scholar
  • Assaf D, Samuel-Cahn E (2000) Simple ratio prophet inequalities for a mortal with multiple choices. J. Appl. Probab. 37(4):1084–1091.CrossrefGoogle Scholar
  • Bruss FT (1988) Invariant record processes and applications to best choice modelling. Stochastic Process Appl. 30(2):303–316.CrossrefGoogle Scholar
  • Bruss FT (2000) Sum the odds to one and stop. Ann. Probab. 28(3):1384–1391.CrossrefGoogle Scholar
  • Bruss FT (2003) A note on bounds for the odds theorem of optimal stopping. Ann. Probab. 31(4):1859–1861.CrossrefGoogle Scholar
  • Bruss FT, Louchard G (2009) The odds algorithm based on sequential updating and its performance. Adv. Appl. Probab. 41(1):131–153.CrossrefGoogle Scholar
  • Bruss FT, Paindaveine D (2000) Selecting a sequence of last successes in independent trials. J. Appl. Probab. 37(2):389–399.CrossrefGoogle Scholar
  • Chow YS, Robbins H, Siegmund DO (1971) Great Expectations: The Theory of Optimal Stopping (Houghton Mifflin, Boston).Google Scholar
  • Ferguson TS (1989) Who solved the secretary problem? Stat. Sci. 4(3):282–296.CrossrefGoogle Scholar
  • Ferguson TS (2006) Optimal Stopping and Applications. Available at http://www.math.ucla.edu/~tom/Stopping/Contents.html.Google Scholar
  • Ferguson TS (2008) The sum-the-odds theorem with application to a stopping game of Sakaguchi. Preprint.Google Scholar
  • Gilbert JP, Mosteller F (1966) Recognizing the maximum of a sequence. J. Amer. Stat. Assoc. 61:35–73.CrossrefGoogle Scholar
  • Gnedin AV (2010) Private communication.Google Scholar
  • Hill TP, Kennedy DP (1992) Sharp inequalities for optimal stopping with rewards based on ranks. Ann. Appl. Probab. 2(2):503–517.CrossrefGoogle Scholar
  • Hill TP, Krengel U (1992) A prophet inequality related to the secretary problem. Contemp. Math. 125:209–215.CrossrefGoogle Scholar
  • Hsiau SR, Yang JR (2002) Selecting the last success in Markov-dependent trials. J. Appl. Probab. 39(2):271–281.CrossrefGoogle Scholar
  • Matsui M, Ano K (2012) Lower bounds for Bruss’ odds problem with multiple stoppings. arXiv:1204.5537v1.Google Scholar
  • Pfeifer D (1989) Extremal processes, secretary problems and the 1/e-law. J. Appl. Probab. 26(4):722–733.CrossrefGoogle Scholar
  • Samuels SM (1992) Secretary problems as a source of benchmark bounds. Shaked M, Tong YL, eds. Stochastic Inequalities, IMS Lecture Notes Monogram Ser., Vol. 22 (IMS, Hayward, CA), 371–387.CrossrefGoogle Scholar
  • Shiryaev AN (2008) Optimal Stopping Rules, Stochastic Modelling and Applied Probability, Vol. 8 (Springer, Berlin).Google Scholar
  • Tamaki M (2010) Sum the multiplicative odds to one and stop. J. Appl. Probab. 47(3):761–777.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.