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

Martín Egozcue1, Luis Fuentes García2, Wing‐Keung Wong3, Ričardas Zitikis4
1Department of Economics, University of Montevideo, Montevideo, Uruguay
2Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, A Coruña, Spain
3Department of Economics and the Institute for Computational Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
4Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Canada

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Balakrishnan N., Lai C.-D., Continuous Bivariate Distributions, 2nd ed., Springer, New York, 2009

Broll U., Egozcue M., Wong W.-K., Zitikis R., Prospect theory, indifference curves, and hedging risks, Appl. Math. Res. Express. AMRX, 2010, 2, 142–153

Cerone P., Dragomir S.S., Mathematical Inequalities, CRC Press, Boca Raton, 2011

Cuadras C.M., On the covariance between functions, J. Multivariate Anal., 2002, 81(1), 19–27

Denuit M., Dhaene J., Goovaerts M., Kaas R., Actuarial Theory for Dependent Risks: Measures, Orders and Models, John Wiley & Sons, Chichester, 2005

Dudley D.M., Norvaiša R., Differentiability of Six Operators on Nonsmooth Functions and p-Variation, Lecture Notes in Math., 1703, Springer, New York, 1999

Dudley D.M., Norvaiša R., Concrete Functional Calculus, Springer Monogr. Math., Springer, New York, 2011

Egozcue M., Fuentes Garcia L., Wong W.-K., On some covariance inequalities for monotonic and non-monotonic functions, JIPAM. J. Inequal. Pure Appl. Math., 2009, 10(3), #75

Egozcue M., Fuentes García L., Wong W.-K., Zitikis R., Grüss-type bounds for the covariance of transformed random variables, J. Inequal. Appl., 2010, ID 619423

Furman E., Zitikis R., Weighted risk capital allocations, Insurance Math. Econom., 2008, 43(2), 263–269

Furman E., Zitikis R., General Stein-type covariance decompositions with applications to insurance and finance, Astin Bull., 2010, 40(1), 369–375

Kowalczyk T., Pleszczynska E., Monotonic dependence functions of bivariate distributions, Ann. Statist., 1977, 5(6), 1221–1227

Lehmann E.L., Some concepts of dependence, Ann. Math. Statist., 1966, 37(5), 1137–1153

Matuła P., On some inequalities for positively and negatively dependent random variables with applications, Publ. Math. Debrecen, 2003, 63(4), 511–522

Matuła P., A note on some inequalities for certain classes of positively dependent random variables, Probab. Math. Statist., 2004, 24(1), 17–26

Matuła P., Ziemba M., Generalized covariance inequalities. Cent. Eur. J. Math., 2011, 9(2), 281–293

McNeil A.J., Frey R., Embrechts P., Quantitative Risk Management, Princet. Ser. Finance, Princeton University Press, Princeton, 2005

Niezgoda M., New bounds for moments of continuous random variables, Comput. Math. Appl., 2010, 60(12), 3130–3138

Wright R., Expectation dependence of random variables, with an application in portfolio theory, Theory and Decision, 1987, 22(2), 111–124

Zitikis R., Grüss’s inequality, its probabilistics interpretation, and a sharper bound, J. Math. Inequal., 2009, 3(1), 15–20