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On inequalities for moments and the covariance of monotone functions

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  • Schmidt, Klaus D.

Abstract

Intuition based on the usual interpretation of the covariance of two random variables suggests that the inequality cov[f(X),g(X)]≥0 should hold for any random variable X and any two increasing functions f and g. The inequality holds indeed, but a proof is hard to find in the literature. In this paper we provide an elementary proof of a more general inequality for moments and we present several applications in actuarial mathematics.

Suggested Citation

  • Schmidt, Klaus D., 2014. "On inequalities for moments and the covariance of monotone functions," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 91-95.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:91-95
    DOI: 10.1016/j.insmatheco.2013.12.006
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    References listed on IDEAS

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    1. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    2. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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