Title: Some remarks on quantiles and distortion risk measures
Authors: Dhaene, Jan
Kukush, Alexander
Linders, Daniƫl
Tang, Qihe
Issue Date: Sep-2012
Publisher: KU Leuven - Faculty of Economics and Business
Series Title: FEB Research Report AFI_1273 pages:1-11
Abstract: Distorted expectations can be expressed as mixtures of quantiles. In this note, we show that this statement is essentially true, but that one has to be careful with
the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that appear in the literature often do not cover the case of a general distortion function. We present a straightforward proof for the general case, making use of the appropriate expressions for distorted expectations in terms of mixtures of quantiles.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Research Center Insurance, Leuven

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