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Lp-metric under the location-independent risk ordering of random variables

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  • Yang, Jianping
  • Zhuang, Weiwei
  • Hu, Taizhong

Abstract

The Lp-metric Δh,p(X) between the survival function F¯ of a random variable X and its distortion h∘F¯ is a characteristic of the variability of X. In this paper, it is shown that if a random variable X is larger than another random variable Y in the location-independent risk order or in the excess wealth order, then Δh,p(X)≥Δh,p(Y) whenever p∈(0,1] and the distortion function h is convex or concave. An alternative and simple proof of the corresponding known result in the literature for the dispersive order is given. Some applications are also presented.

Suggested Citation

  • Yang, Jianping & Zhuang, Weiwei & Hu, Taizhong, 2014. "Lp-metric under the location-independent risk ordering of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 321-324.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:321-324
    DOI: 10.1016/j.insmatheco.2014.10.009
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    References listed on IDEAS

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    1. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    2. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    3. Michael Landsberger & Isaac Meilijson, 1994. "The Generating Process and an Extension of Jewitt's Location Independent Risk Concept," Management Science, INFORMS, vol. 40(5), pages 662-669, May.
    4. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    5. Mao, Tiantian & Hu, Taizhong, 2012. "Characterization of left-monotone risk aversion in the RDEU model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 413-422.
    6. Hu, Taizhong & Chen, Jing & Yao, Junchao, 2006. "Preservation of the location independent risk order under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 406-412, April.
    7. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
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    Cited by:

    1. Sordo, Miguel A. & Castaño-Martínez, Antonia & Pigueiras, Gema, 2016. "A family of premium principles based on mixtures of TVaRs," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 397-405.
    2. 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.
    3. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    4. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    5. Yang, Jianping & Hu, Taizhong, 2016. "New developments on the Lp-metric between a probability distribution and its distortion," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 236-243.
    6. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.

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