On inequalities for moments and the covariance of monotone functions

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.

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Year of publication:	2014
Authors:	Schmidt, Klaus D.
Published in:	Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 55.2014, C, p. 91-95
Publisher:	Elsevier
Subject:	Correlation \| Comonotonicity \| Risk measures \| Esscher premium \| Collective model \| Reinsurance

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011046633