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Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures

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  • Cai, Jun
  • Wang, Ying
  • Mao, Tiantian

Abstract

In this paper, we extend the concept of tail subadditivity (Belles-Sampera et al., 2014a; Belles-Sampera et al., 2014b) for distortion risk measures and give sufficient and necessary conditions for a distortion risk measure to be tail subadditive. We also introduce the generalized GlueVaR risk measures, which can be used to approach any coherent distortion risk measure. To further illustrate the applications of the tail subadditivity, we propose multivariate tail distortion (MTD) risk measures and generalize the multivariate tail conditional expectation (MTCE) risk measure introduced by Landsman et al. (2016). The properties of multivariate tail distortion risk measures, such as positive homogeneity, translation invariance, monotonicity, and subadditivity, are discussed as well. Moreover, we discuss the applications of the multivariate tail distortion risk measures in capital allocations for a portfolio of risks and explore the impacts of the dependence between risks in a portfolio and extreme tail events of a risk portfolio in capital allocations.

Suggested Citation

  • Cai, Jun & Wang, Ying & Mao, Tiantian, 2017. "Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 105-116.
    • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:105-116
    DOI: 10.1016/j.insmatheco.2017.05.004
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    References listed on IDEAS

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    11. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
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    1. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Risk measurement of joint risk of portfolios: a liquidity shortfall aspect," Papers 2212.04848, arXiv.org, revised May 2024.
    2. Cai, Jun & Wang, Ying, 2021. "Optimal capital allocation principles considering capital shortfall and surplus risks in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 329-349.
    3. Cornilly, D. & Rüschendorf, L. & Vanduffel, S., 2018. "Upper bounds for strictly concave distortion risk measures on moment spaces," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 141-151.
    4. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    5. Haoyu Chen & Kun Fan, 2022. "Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    6. Baishuai Zuo & Chuancun Yin, 2022. "Doubly truncated moment risk measures for elliptical distributions," Papers 2203.01091, arXiv.org.
    7. Ling, Chengxiu, 2019. "Asymptotics of multivariate conditional risk measures for Gaussian risks," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 205-215.
    8. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    9. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
    10. Shushi, Tomer & Yao, Jing, 2020. "Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 178-186.
    11. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.

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