Grüss-type bounds for the covariance of transformed random variables

Ričardas Zitikis*, Martín Egozcue, Luis Fuentes García, Wing Keung WONG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

A number of problems in Economics, Finance, Information Theory, Insurance, and generally in decision making under uncertainty rely on estimates of the covariance between (transformed) random variables, which can, for example, be losses, risks, incomes, financial returns, and so forth. Several avenues relying on inequalities for analyzing the covariance are available in the literature, bearing the names of Chebyshev, Grüss, Hoeffding, Kantorovich, and others. In the present paper we sharpen the upper bound of a Grüss-type covariance inequality by incorporating a notion of quadrant dependence between random variables and also utilizing the idea of constraining the means of the random variables.

Original languageEnglish
Article number619423
JournalJournal of Inequalities and Applications
Volume2010
DOIs
Publication statusPublished - 2010

Scopus Subject Areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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