Asymptotic Duration for Optimal Multiple Stopping Problems

We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an o...
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Autor*in:	Hugh N. Entwistle [verfasserIn] Christopher J. Lustri [verfasserIn] Georgy Yu. Sofronov [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	sequential decision analysis optimal stopping multiple optimal stopping secretary problems asymptotic approximations

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 12(2024), 5, p 652
Übergeordnetes Werk:	volume:12 ; year:2024 ; number:5, p 652

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DOI / URN:	10.3390/math12050652

Katalog-ID:	DOAJ091248892

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520			\|a We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations.
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allfieldsSound	10.3390/math12050652 doi (DE-627)DOAJ091248892 (DE-599)DOAJ10af30dcd37942c6bfd689dfe864c1ed DE-627 ger DE-627 rakwb eng QA1-939 Hugh N. Entwistle verfasserin aut Asymptotic Duration for Optimal Multiple Stopping Problems 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations. sequential decision analysis optimal stopping multiple optimal stopping secretary problems asymptotic approximations Mathematics Christopher J. Lustri verfasserin aut Georgy Yu. Sofronov verfasserin aut In Mathematics MDPI AG, 2013 12(2024), 5, p 652 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:5, p 652 https://doi.org/10.3390/math12050652 kostenfrei https://doaj.org/article/10af30dcd37942c6bfd689dfe864c1ed kostenfrei https://www.mdpi.com/2227-7390/12/5/652 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 5, p 652
language	English
source	In Mathematics 12(2024), 5, p 652 volume:12 year:2024 number:5, p 652
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callnumber-first	Q - Science
author	Hugh N. Entwistle
spellingShingle	Hugh N. Entwistle misc QA1-939 misc sequential decision analysis misc optimal stopping misc multiple optimal stopping misc secretary problems misc asymptotic approximations misc Mathematics Asymptotic Duration for Optimal Multiple Stopping Problems
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topic_title	QA1-939 Asymptotic Duration for Optimal Multiple Stopping Problems sequential decision analysis optimal stopping multiple optimal stopping secretary problems asymptotic approximations
topic	misc QA1-939 misc sequential decision analysis misc optimal stopping misc multiple optimal stopping misc secretary problems misc asymptotic approximations misc Mathematics
topic_unstemmed	misc QA1-939 misc sequential decision analysis misc optimal stopping misc multiple optimal stopping misc secretary problems misc asymptotic approximations misc Mathematics
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title	Asymptotic Duration for Optimal Multiple Stopping Problems
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title_auth	Asymptotic Duration for Optimal Multiple Stopping Problems
abstract	We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations.
abstractGer	We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations.
abstract_unstemmed	We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations.
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Asymptotic Duration for Optimal Multiple Stopping Problems

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