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Jackknife empirical likelihood method for some risk measures and related quantities

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  • Peng, Liang
  • Qi, Yongcheng
  • Wang, Ruodu
  • Yang, Jingping
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    Abstract

    Quantifying risks is of importance in insurance. In this paper, we employ the jackknife empirical likelihood method to construct confidence intervals for some risk measures and related quantities studied by Jones and Zitikis (2003). A simulation study shows the advantages of the new method over the normal approximation method and the naive bootstrap method.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 1 ()
    Pages: 142-150

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:142-150

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Confidence interval; Jackknife empirical likelihood; Risk measure;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 22(2), pages 145-161, June.
    3. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(1), pages 137-151, January.
    4. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 17(1), pages 43-54, August.
    5. Bruce L. Jones & Ricardas Zitikis, 2005. "Testing for the order of risk measures: an application of L-statistics in actuarial science," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 193-211.
    6. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(1), pages 49-58, August.
    7. Lynn Wirch, Julia & Hardy, Mary R., 1999. "A synthesis of risk measures for capital adequacy," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 25(3), pages 337-347, December.
    8. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 21(2), pages 173-183, November.
    9. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
    10. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 41(2), pages 279-297, September.
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    Cited by:
    1. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers, Xarxa de Referència en Economia Aplicada (XREAP) XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    2. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers, Universitat de Barcelona, UB Riskcenter 2014-05, Universitat de Barcelona, UB Riskcenter.
    3. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 52(2), pages 255-262.

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