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A family of variability measures based on the cumulative residual entropy and distortion functions

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  • Psarrakos, Georgios
  • Toomaj, Abdolsaeed
  • Vliora, Polyxeni

Abstract

Variability measures are important tools in the construction of premium principles and risk aversions. In this paper, we propose a family of such measures based on a distorted weighted cumulative residual entropy, which follows by a sensitivity analysis of distortion risk measures. For this family, we obtain properties, connections with other measures, a covariance representation, and some useful interpretations. Furthermore, we explore an application on premium principles based on beta generated distributions, and we give an empirical estimation. We also provide bounds and numerical illustrations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:212-222
    DOI: 10.1016/j.insmatheco.2023.12.002
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    Cited by:

    1. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.

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    More about this item

    Keywords

    Variability measures; Distortion functions; Cumulative residual entropy; Mean residual life function; Ageing classes;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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