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Tail asymptotics of generalized deflated risks with insurance applications

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  • Ling, Chengxiu
  • Peng, Zuoxiang

Abstract

Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{XκI{SX>x}} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck–Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.

Suggested Citation

  • Ling, Chengxiu & Peng, Zuoxiang, 2016. "Tail asymptotics of generalized deflated risks with insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 220-231.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:220-231
    DOI: 10.1016/j.insmatheco.2016.09.012
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    References listed on IDEAS

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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Tang, Qihe & Yang, Fan, 2014. "Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 311-320.
    3. Hashorva, Enkelejd & Ling, Chengxiu & Peng, Zuoxiang, 2014. "Second-order tail asymptotics of deflated risks," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 88-101.
    4. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
    5. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    6. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
    7. Ruodu Wang & Johanna F. Ziegel, 2014. "Distortion Risk Measures and Elicitability," Papers 1405.3769, arXiv.org, revised May 2014.
    8. Mao, Tiantian & Hu, Taizhong, 2012. "Second-order properties of the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 333-343.
    9. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
    10. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.
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    More about this item

    Keywords

    Deflated risks; Expectile; Haezendonck–Goovaerts risk measure; Second-order/third-order regular variations; Extreme value theory;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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