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Nonparametric inference for distortion risk measures on tail regions

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  • Hou, Yanxi
  • Wang, Xing

Abstract

Suppose X is some interesting loss and Y is a benchmark variable. Given some extreme scenarios of Y, it is indispensable to measure the tail risk of X by applying a class of univariate risk measures to study the co-movement of the two variables. In this paper, we consider the extreme and nonparametric inference for the distortion risk measures on the tail regions when the extreme scenarios of some benchmark variable are considered. We derive the limit of the proposed risk measures based on Extreme Value Theory. The asymptotics of the risk measures shows the decomposition of the marginal extreme value index and the extreme dependence structure which implies how these two pieces of information have influences on the limit of the risk measures. Finally, for practical purpose, we develop a nonparametric estimation method for the distortion risk measures on tail regions and its asymptotic normality is derived.

Suggested Citation

  • Hou, Yanxi & Wang, Xing, 2019. "Nonparametric inference for distortion risk measures on tail regions," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 92-110.
    • Handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:92-110
    DOI: 10.1016/j.insmatheco.2019.09.003
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    1. Juan-Juan Cai & John H. J. Einmahl & Laurens Haan & Chen Zhou, 2015. "Estimation of the marginal expected shortfall: the mean when a related variable is extreme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 417-442, March.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2017. "Measuring Systemic Risk," The Review of Financial Studies, Society for Financial Studies, vol. 30(1), pages 2-47.
    4. Belles-Sampera, Jaume & Guillen, Montserrat & Santolino, Miguel, 2016. "What attitudes to risk underlie distortion risk measure choices?," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 101-109.
    5. Laurence Carassus & Miklós Rásonyi, 2015. "On Optimal Investment For A Behavioral Investor In Multiperiod Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 115-153, January.
    6. Billio, Monica & Getmansky, Mila & Lo, Andrew W. & Pelizzon, Loriana, 2012. "Econometric measures of connectedness and systemic risk in the finance and insurance sectors," Journal of Financial Economics, Elsevier, vol. 104(3), pages 535-559.
    7. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    8. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    9. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    10. Zhu, Li & Li, Haijun, 2012. "Tail distortion risk and its asymptotic analysis," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 115-121.
    11. Glenn W. Harrison & J. Todd Swarthout, 2016. "Cumulative Prospect Theory in the Laboratory: A Reconsideration," Experimental Economics Center Working Paper Series 2016-04, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    12. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    13. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
    14. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    15. Asimit, Alexandru V. & Li, Jinzhu, 2016. "Extremes for coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 332-341.
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    Cited by:

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    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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