Open Access Research Article

Grüss-Type Bounds for the Covariance of Transformed Random Variables

Martín Egozcue12, Luis Fuentes García3, Wing-Keung Wong4 and Ričardas Zitikis5*

Author Affiliations

1 Department of Economics, University of Montevideo, Montevideo 11600, Uruguay

2 Accounting and Finance Department, Norte Construcciones, Punta del Este 20100, Uruguay

3 Departamento de Métodos Matemáticos e de Representación, Escola Técnica Superior de Enxeñeiros de Camiños, Canais e Portos, Universidade da Coruña, 15001 A Coruña, Spain

4 Department of Economics, Institute for Computational Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

5 Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada, N6A 5B7

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Journal of Inequalities and Applications 2010, 2010:619423  doi:10.1155/2010/619423

Published: 28 March 2010

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.