A multiple optimal stopping rule for sums of independent random variables

2007 ◽  
Vol 17 (5) ◽  
Author(s):  
M. L. Nikolaev ◽  
G. Yu. Sofronov
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Independent Random Variables ◽  
Optimal Stopping Rule

scholarly journals An optimal sequential procedure for a buying-selling problem with independent observations

2006 ◽  
Vol 43 (02) ◽  
pp. 454-462 ◽  
Author(s):  
G. Sofronov ◽  
Jonathan M. Keith ◽  
Dirk P. Kroese
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Sequential Procedure ◽  
Independent Random Variables ◽  
Value Of A Game ◽  
Optimal Stopping Rule ◽  
Independent Observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

scholarly journals An optimal sequential procedure for a buying-selling problem with independent observations

2006 ◽  
Vol 43 (2) ◽  
pp. 454-462 ◽  
Author(s):  
G. Sofronov ◽  
Jonathan M. Keith ◽  
Dirk P. Kroese
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Stopping Rule ◽  
Sequential Procedure ◽  
Independent Random Variables ◽  
Value Of A Game ◽  
Optimal Stopping Rule ◽  
Independent Observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

On the Sequential Detection Problem

1989 ◽  
Vol 38 (3-4) ◽  
pp. 129-146
Author(s):  
Uttam Bandyopadhyay
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Stopping Rule ◽  
Independent Random Variables ◽  
Sequential Detection ◽  
Detection Problem ◽  
Asymptotic Results ◽  
Rule Based ◽  
Unknown Point ◽  
Cumulative Sums

In this paper, for an infinite sequence of independent random variables, we have considered the problem of estimation of an unknown point ( q) where a change in the distribution of the random variables occurs. Attaching suitable scores for the observed values. of the random variables, a stopping rule based on the cumulative sums of these scores has been proposed. Some asymptotic results useful for studying the performance of the proposed procedure havo beon obtained.

A Multiple Stopping Problem

1994 ◽  
Vol 8 (2) ◽  
pp. 169-177 ◽  
Author(s):  
J. Preater
Keyword(s):  
Optimal Stopping ◽  
Stopping Rule ◽  
Reward Function ◽  
Optimal Stopping Rule ◽  
Multiple Stopping ◽  
Constant Observation ◽  
Independent And Identically Distributed

In the context of team recruitment, we discuss an optimal multiple stopping problem for an infinite independent and identically distributed sequence, with general reward function and constant observation cost. We establish the existence and nature of an optimal stopping rule. For the particular case where team quality is governed by the fitness of the weakest member, we show that the recruiter should be more discriminating with either a better, or a larger, group of appointees in hand.

scholarly journals OPTIMAL SELECTION OF THE k-TH BEST CANDIDATE

2019 ◽  
Vol 33 (3) ◽  
pp. 327-347
Author(s):  
Yi-Shen Lin ◽  
Shoou-Ren Hsiau ◽  
Yi-Ching Yao
Keyword(s):  
Optimal Stopping ◽  
Stopping Rule ◽  
Secretary Problem ◽  
Optimal Selection ◽  
Maximum Probability ◽  
Optimal Stopping Rule ◽  
The Subject ◽  
Selection Of

In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of n candidates when their relative ranks are observed sequentially. This problem has been extended to optimally selecting the kth best candidate for k ≥ 2. While the optimal stopping rule for k=1,2 (and all n ≥ 2) is known to be of threshold type (involving one threshold), we solve the case k=3 (and all n ≥ 3) by deriving an explicit optimal stopping rule that involves two thresholds. We also prove several inequalities for p(k, n), the maximum probability of selecting the k-th best of n candidates. It is shown that (i) p(1, n) = p(n, n) > p(k, n) for 1<k<n, (ii) p(k, n) ≥ p(k, n + 1), (iii) p(k, n) ≥ p(k + 1, n + 1) and (iv) p(k, ∞): = lim n→∞p(k, n) is decreasing in k.

OPTIMAL STOPPING IN A STOCHASTIC GAME

2008 ◽  
Vol 23 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Bahar Kaynar
Keyword(s):  
Optimal Stopping ◽  
Stochastic Game ◽  
Stopping Rule ◽  
The Other ◽  
Random Numbers ◽  
Optimal Stopping Rule

In this article we consider a stochastic game in which each player draws one or two random numbers between 0 and 1. Players can decide to stop after the first draw or to continue for a second draw. The decision is made without knowing the other players’ numbers or whether the other players continue for a second draw. The object of the game is to have the highest total score without going over 1. In the article, we will characterize the optimal stopping rule for each player.

Recognizing both the maximum and the second maximum of a sequence

1979 ◽  
Vol 16 (4) ◽  
pp. 803-812 ◽  
Author(s):  
M. Tamaki
Keyword(s):  
Decision Maker ◽  
Optimal Stopping ◽  
Stopping Rule ◽  
Maximum Probability ◽  
Second Best ◽  
Optimal Stopping Rule

We consider the situation in which the decision-maker is allowed to have two choices and he must choose both the best and the second best from a group of N applicants. The optimal stopping rule and the maximum probability of choosing both of them are derived.

Stopping rules for proofreading

1989 ◽  
Vol 26 (02) ◽  
pp. 304-313 ◽  
Author(s):  
T. S. Ferguson ◽  
J. P. Hardwick
Keyword(s):  
Sample Size ◽  
Optimal Stopping ◽  
Random Number ◽  
Poisson Model ◽  
Stopping Rule ◽  
Stopping Rules ◽  
Binomial Model ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
Optimal Stopping Rule

A manuscript with an unknown random numberMof misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On thenthproofreading, each remaining misprint is detected independently with probabilitypn– 1. Each proofreading costs an amountCP&gt; 0, and if one stops afternproofreadings, each misprint overlooked costs an amountcn&gt; 0. Two models are treated based on the distribution ofM.In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.

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