Maximizing \(E\max _{1\leq k\leq n}S^+_ k/ES^+_ n:\) A prophet inequality for sums of i.i.d. mean zero variates (Q1825517)
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scientific article; zbMATH DE number 4121140
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximizing \(E\max _{1\leq k\leq n}S^+_ k/ES^+_ n:\) A prophet inequality for sums of i.i.d. mean zero variates |
scientific article; zbMATH DE number 4121140 |
Statements
Maximizing \(E\max _{1\leq k\leq n}S^+_ k/ES^+_ n:\) A prophet inequality for sums of i.i.d. mean zero variates (English)
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1989
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Let \(X_ 1,X_ 2,..\). be i.i.d. mean zero random variables. Put \(S_ k=X_ 1+...+X_ k\). It is proved that for any \(n\geq 1\) \[ E(\max_{1\leq k\leq n\quad}S^+_ k)\leq (2-n^{-1})E S\quad^+_ n. \] This result is nearly sharp.
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optimal stopping
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prophet inequality
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