On Asymptotics of Optimal Stopping Times

Hugh N. Entwistle, Christopher J. Lustri and Georgy Yu. Sofronov
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Hugh N. Entwistle: Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia
Christopher J. Lustri: Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia
Georgy Yu. Sofronov: Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia

Mathematics, 2022, vol. 10, issue 2, 1-18

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.

Keywords: sequential decision analysis; optimal stopping; secretary problems; asymptotic approximations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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