Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 619423, 10 pages
doi:10.1155/2010/619423
Research Article

Grüss-Type Bounds for the Covariance of Transformed Random Variables

Martín Egozcue,1,2 Luis Fuentes García,3 Wing-Keung Wong,4 and Ričardas Zitikis5

1Department of Economics, University of Montevideo, Montevideo 11600, Uruguay
2Accounting and Finance Department, Norte Construcciones, Punta del Este 20100, Uruguay
3Departamento de Métodos Matemáticos e de Representación, Escola Técnica Superior de Enxeñeiros de Camiños, Canais e Portos, Universidade da Coruña, 15001 A Coruña, Spain
4Department of Economics, Institute for Computational Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
5Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, Canada

Received 9 November 2009; Revised 28 February 2010; Accepted 16 March 2010

Academic Editor: Soo Hak Sung

Copyright © 2010 Martín Egozcue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.