# Sum the Multiplicative Odds to One and Stop

@article{Tamaki2010SumTM, title={Sum the Multiplicative Odds to One and Stop}, author={M. Tamaki}, journal={Journal of Applied Probability}, year={2010}, volume={47}, pages={761 - 777} }

We consider the optimal stopping problem of maximizing 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 such that 1 ≤ m < n. The optimal stopping rule of this problem has a nice interpretation, that is, it stops on the first success for which the sum of the m-fold multiplicative odds of success for the future trials is less than or equal to 1. This result can be viewed as a…

## 13 Citations

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

- MathematicsJournal of Applied Probability
- 2014

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…

The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi

- Mathematics
- 2016

The optimal stopping problem of maximizing the probability of stopping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and…

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

- Computer ScienceJ. Appl. Probab.
- 2014

A bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory is presented, attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

Maximizing the probability of stopping on any of the last m successes in independent Bernoulli trials with random horizon

- MathematicsAdvances in Applied Probability
- 2011

We consider the problem of maximizing the probability of stopping on any of the last m successes in independent Bernoulli trials with random horizon of length N, where m is a predetermined integer. A…

Weber's optimal stopping problem and generalizations

- Mathematics
- 2013

One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe n independent indicator variables I1,I2,…,In sequentially and we…

Optimal Stopping Rule for the No-Information Duration Problem with Random Horizon

- Mathematics, Computer ScienceAdvances in Applied Probability
- 2013

This paper generalizes the classical duration problem in two directions by allowing the number N to be a random variable with a known upper bound n and also allowing the objects to appear in accordance with Bernoulli trials.

Stochastic Input Models in Online Computing

- Mathematics, Computer ScienceArXiv
- 2017

This paper studies twelve stochastic input models for online problems and reveals the relationships among the competitive ratios for the models, and considers two basic online problems, which are variants of the secretary problem and the prophet inequality problem, under the models.

Journal of Applied Probability Volume 47 (2010): Index

- Journal of Applied Probability
- 2010

pages Allaart, P. A general ‘bang–bang’ principle for predicting the maximum of a random walk . . . . . 1072–1083 Alodat, M. T., Al-Rawwash, M. and Jebrini, M. A. Duration distribution of the…

Dynamic Programming and Linear Programming for Odds Problem

- Mathematics
- 2021

This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the…

Stochastic processes with proportional increments and the last-arrival problem

- Mathematics
- 2012

The notion of stochastic processes with proportional increments is introduced. This notion is of general interest as indicated by its relationship with several stochastic processes, as counting…

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