On a family of coherent measures of variability

Abstract

Risk measures are important and widely used tools in quantitative risk management of insurance companies and financial institutions. In this paper, we will introduce a family of coherent variability measures with comonotonic additivity, which is based on Lr-metric between a probability distribution and its distortion. One of its special cases is the cumulative residual entropy of a distribution. Further properties and potential applications of these coherent variability measures are presented. More attention is paid on composing a new coherent risk measure from expected shortfall and tail cumulative residual entropy to capture tail risk.