Recognizing the maximum of a random sequence based on relative rank with backward solicitation

1974 ◽  
Vol 11 (3) ◽  
pp. 504-512 ◽  
Author(s):  
Mark C. K. Yang
Keyword(s):  
General Formula ◽  
Optimal Stopping ◽  
Random Sequence ◽  
Geometric Probability ◽  
Secretary Problem ◽  
Stopping Rules ◽  
Relative Rank ◽  
Special Cases ◽  
Optimal Stopping Rules

The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.

Recognizing the maximum of a random sequence based on relative rank with backward solicitation

1974 ◽  
Vol 11 (03) ◽  
pp. 504-512 ◽  
Author(s):  
Mark C. K. Yang
Keyword(s):  
General Formula ◽  
Optimal Stopping ◽  
Random Sequence ◽  
Geometric Probability ◽  
Secretary Problem ◽  
Stopping Rules ◽  
Relative Rank ◽  
Special Cases ◽  
Optimal Stopping Rules

The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.

Optimal stopping rules for directionally reinforced processes

2001 ◽  
Vol 33 (2) ◽  
pp. 483-504 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino
Keyword(s):  
Transaction Costs ◽  
Optimal Stopping ◽  
Optimal Strategies ◽  
Stopping Rules ◽  
Elementary Model ◽  
Numerical Examples ◽  
Special Cases ◽  
Correlated Random Walks ◽  
Multiple Stopping ◽  
Optimal Stopping Rules

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement behavior. Explicit descriptions of optimal stopping rules are given in several interesting special cases with and without transaction costs. Numerical examples are presented comparing optimal strategies to simpler buy and hold strategies.

Optimal stopping rules for correlated random walks with a discount

2004 ◽  
Vol 41 (2) ◽  
pp. 483-496 ◽  
Author(s):  
Pieter Allaart
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Optimal Stopping ◽  
Constant Factor ◽  
Stopping Rules ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
Optimal Rule ◽  
Correlated Random Walks ◽  
Optimal Stopping Rules

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

Optimal stopping rules in proofreading

1982 ◽  
Vol 19 (3) ◽  
pp. 723-729 ◽  
Author(s):  
Mark C. K. Yang ◽  
Dennis D. Wackerly ◽  
Andrew Rosalsky
Keyword(s):  
Optimal Stopping ◽  
Stopping Rules ◽  
Optimal Stopping Rules

Optimal stopping rules under various conditions are obtained for a proofreader who has a probability p (known or unknown) of detecting a misprint in proofsheets which contain an unknown but Poisson-distributed number of misprints.

On the best-choice problem when the number of observations is random

1983 ◽  
Vol 20 (1) ◽  
pp. 165-171 ◽  
Author(s):  
Joseph D. Petruccelli
Keyword(s):  
Optimal Stopping ◽  
Random Variable ◽  
Stopping Rules ◽  
Necessary And Sufficient Condition ◽  
Choice Problem ◽  
Best Choice Problem ◽  
Optimal Stopping Rule ◽  
Optimal Stopping Rules ◽  
Bounded Random Variable ◽  
Necessary And Sufficient

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.

Optimal stopping rules for directionally reinforced processes

2001 ◽  
Vol 33 (2) ◽  
pp. 483-504 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino
Keyword(s):  
Optimal Stopping ◽  
Stopping Rules ◽  
Optimal Stopping Rules
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