On inequalities for moments and the covariance of monotone functions

Klaus D. Schmidt

Insurance: Mathematics and Economics, 2014, vol. 55, issue C, 91-95

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.

Keywords: Correlation; Comonotonicity; Risk measures; Esscher premium; Collective model; Reinsurance (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:55:y:2014:i:c:p:91-95

DOI: 10.1016/j.insmatheco.2013.12.006

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