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Second-order tail asymptotics of deflated risks

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  • Hashorva, Enkelejd
  • Ling, Chengxiu
  • Peng, Zuoxiang

Abstract

Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:56:y:2014:i:c:p:88-101
    DOI: 10.1016/j.insmatheco.2014.04.003
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    References listed on IDEAS

    as
    1. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    2. Beirlant, J. & Dierckx, G. & Guillou, A., 2011. "Bias-reduced estimators for bivariate tail modelling," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 18-26, July.
    3. Zhu, Li & Li, Haijun, 2012. "Tail distortion risk and its asymptotic analysis," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 115-121.
    4. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    5. 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.
    6. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    7. 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.
    8. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
    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.
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    Cited by:

    1. 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.
    2. Prieto, Marc & Caemmerer, Barbara & Baltas, George, 2015. "Using a hedonic price model to test prospect theory assertions: The asymmetrical and nonlinear effect of reliability on used car prices," Journal of Retailing and Consumer Services, Elsevier, vol. 22(C), pages 206-212.

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    More about this item

    Keywords

    Random deflation; Value-at-Risk; Risk aggregation; Second-order regular variation; Estimation of tail probability;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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