scholarly journals Logconcave reward functions and optimal stopping rules of threshold form

2014 ◽  
Vol 19 (0) ◽  
Author(s):  
Shoou-Ren Hsiau ◽  
Yi-Shen Lin ◽  
Yi-Ching Yao
Keyword(s):  
Optimal Stopping ◽  
Stopping Rules ◽  
Optimal Stopping Rules ◽  
Reward Functions

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

Search models

1992 ◽  
Vol 29 (3) ◽  
pp. 605-615 ◽  
Author(s):  
J. A. Bather
Keyword(s):  
Mathematical Models ◽  
Optimal Stopping ◽  
Poisson Processes ◽  
Stopping Rules ◽  
Stopping Times ◽  
Oil Exploration ◽  
Search Models ◽  
Number Of Components ◽  
Optimal Stopping Rules ◽  
Optimal Stopping Times

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here we consider a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.

scholarly journals Behaviorally consistent optimal stopping rules

1990 ◽  
Vol 51 (2) ◽  
pp. 391-402 ◽  
Author(s):  
Edi Karni ◽  
Zvi Safra
Keyword(s):  
Optimal Stopping ◽  
Stopping Rules ◽  
Optimal Stopping Rules

Optimal Stopping Rules For Some Blackjack Type Problems

2010 ◽  
Author(s):  
Andrzej Z. Grzybowski ◽  
Alexander M. Korsunsky
Keyword(s):  
Optimal Stopping ◽  
Stopping Rules ◽  
Optimal Stopping Rules
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