An optimal stopping problem with finite horizon for sums of i.i.d. random variables
type: Item
instance of: scholarly article
title: An optimal stopping problem with finite horizon for sums of i.i.d. random variables
zbMATH Open document ID: 0636.60046
DOI: 10.1016/0304-4149(87)90054-8
author: Wolfgang Stadje
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: For a sequence \(U_ 1,U_ 2,..\). of i.i.d. random variables with zero expectation and unit variance, the optimal stopping problem for \((n- j)^{\ell}(U_ 1+...+U_ j)\), \(1\leq j\leq n\), \(\ell\) some fixed positive integer, is treated. Using backward induction, the general structure of the optimal stopping time is obtained. Furthermore, by considering the corresponding stopping problem for Brownian motion which may be explicitly solved using a time-change argument, the author derives the asymptotic behaviour of the optimal stopping time as n tends to infinity.
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 4036828
zbMATH Keywords: finite horizon
zbMATH Keywords: optimal stopping problem
zbMATH Keywords: stopping problem for Brownian motion
zbMATH Keywords: asymptotic behaviour of the optimal stopping time
reviewed by: Albrecht Irle
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90054-8
OpenAlex ID: W1985460312
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description: scientific article; zbMATH DE number 4036828