Chebyshev inequalities with law-invariant deviation measures

Bogdan Grechuk, Anton Molyboha, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The consistency of law-invariant general deviation measures with concave ordering has been used to generalize the RaoBlackwell theorem and to develop an approach for reducing minimization of law-invariant deviation measures to minimization of the measures on subsets of undominated random variables with respect to concave ordering. This approach has been applied for constructing the Chebyshev and Kolmogorov inequalities with law-invariant deviation measuresin particular with mean absolute deviation, lower semideviation and conditional value-at-risk deviation. Additionally, an advantage of the Kolmogorov inequality with certain deviation measures has been illustrated in estimating the probability of the exchange rate of two currencies to be within specified bounds.

Original languageEnglish
Pages (from-to)145-170
Number of pages26
JournalProbability in the Engineering and Informational Sciences
Volume24
Issue number1
DOIs
StatePublished - Jan 2010

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