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A prophet inequality for independent random variables with finite variances

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

D. P. Kennedy  and
R. P. Kertz
D. P. Kennedy*
Affiliation:
University of Cambridge
R. P. Kertz*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
∗∗Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

It is demonstrated that for each n ≧ 2 there exists a minimal universal constant, cn, such that, for any sequence of independent random variables {Xr, r ≧ 1} with finite variances, , where the supremum is over all stopping times Τ, 1 ≦ Τ ≦ n. Furthermore, cn ≦ 1/2 and lim infn→ ∞cn ≧ 0.439485 · ··.

Keywords

OPTIMAL STOPPINGPROPHET INEQUALITY

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 945 - 958
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Supported in part by NSF grant DMS 92-09586.

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