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Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

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Central European Journal of Mathematics

Abstract

We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance.

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Authors and Affiliations

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

    Martín Egozcue

  2. Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, 15001, A Coruña, Spain

    Luis Fuentes García

  3. Department of Economics and the Institute for Computational Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Wing-Keung Wong

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

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Authors
  1. Martín Egozcue
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  2. Luis Fuentes García
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  3. Wing-Keung Wong
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  4. Ričardas Zitikis
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Correspondence to Martín Egozcue.

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Egozcue, M., García, L.F., Wong, WK. et al. Grüss-type bounds for covariances and the notion of quadrant dependence in expectation. centr.eur.j.math. 9, 1288–1297 (2011). https://doi.org/10.2478/s11533-011-0088-x

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  • DOI: https://doi.org/10.2478/s11533-011-0088-x

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