On asymptotics of optimal stopping times

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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; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes 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 these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.
LanguageEnglish
Number of pages14
JournalarXiv e-prints
Publication statusSubmitted - 5 Apr 2019

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Optimal Stopping Time
Upper bound
Asymptotic Behavior
Statistics
Optimal Stopping Problem
Independent Random Variables
Reward
Decay Rate
Probability density function
Probability Distribution
Maximise

Cite this

Lustri, C., & Sofronov, G. (2019). On asymptotics of optimal stopping times. Manuscript submitted for publication.
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On asymptotics of optimal stopping times. / Lustri, Christopher; Sofronov, Georgy.

In: arXiv e-prints, 05.04.2019.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Sofronov, Georgy

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N2 - 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; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes 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 these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

AB - 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; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes 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 these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

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