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Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations
Holger Kösters
Source: Ann. Probab. Volume 32, Number 4 (2004), 3324-3332.
Abstract
Let X1,X2,… be a sequence of [0,1]-valued i.i.d. random variables, let c≥0 be a sampling cost for each observation and let Yi=Xi−ic, i=1,2,…. For n=1,2,…, let M(Y1,…,Yn)=E(max 1≤i≤nYi) and V(Y1,…,Yn)=sup τ∈CnE(Yτ), where Cn denotes the set of all stopping rules for Y1,…,Yn. Sharp upper bounds for the difference M(Y1,…,Yn)−V(Y1,…,Yn) are given under various restrictions on c and n.
Primary Subjects: 60G40
Secondary Subjects: 60E15
Keywords: Prophet inequality; optimal stopping
Full-text: Access granted (open access)
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1107883355
Digital Object Identifier: doi:10.1214/009117904000000496
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