On asymptotics of optimal stopping times

Hugh N. Entwistle, Christopher J. Lustri, Georgy Yu Sofronov*

*Corresponding author for this work

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    Abstract

    We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.
    Original languageEnglish
    Article number194
    Pages (from-to)1-18
    Number of pages18
    JournalMathematics
    Volume10
    Issue number2
    DOIs
    Publication statusPublished - 2 Jan 2022

    Bibliographical note

    Copyright the Author(s) 2022. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

    Keywords

    • sequential decision analysis
    • optimal stopping
    • secretary problems
    • asymptotic approximations

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