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Optimal Stopping Under General Dependence Conditions

Published online by Cambridge University Press:  20 November 2018

M. Longnecker
M. Longnecker*
Affiliation:
Texas A & M University, College Station, Texas 77843
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Abstract

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Let {Xn} be a sequence of random variables, not necessarily independent or identically distributed, put and Mn =max0≤k≤n|Sk|. Effective bounds on in terms of assumed bounds on , are used to identify conditions under which an extended-valued stopping time τ exists. That is these inequalities are used to guarantee the existence of the stopping time τ such that E(ST/aτ) = supt ∈ T∞ E(|Sτ|/at), where T∞ denotes the class of randomized extended-valued stopping times based on S1, S2, … and {an} is a sequence of constants. Specific applications to stochastic processes of the time series type are considered.

Keywords

60G4062L15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 260 - 266
Copyright
Copyright © Canadian Mathematical Society 1983

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