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On a family of coherent measures of variability

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  • Hu, Taizhong
  • Chen, Ouxiang

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.

Suggested Citation

  • Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    • Handle: RePEc:eee:insuma:v:95:y:2020:i:c:p:173-182
    DOI: 10.1016/j.insmatheco.2020.10.005
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    Cited by:

    1. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    2. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.

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    More about this item

    Keywords

    Risk measure; Variability measure; Cumulative residual entropy; CRE-Shortfall; Distortion;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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