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Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions

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  • Deme, El Hadji
  • Girard, Stéphane
  • Guillou, Armelle

Abstract

Many different premium principles have been proposed in the literature. In this paper, we focus on the Proportional Hazard Premium. Its asymptotic normality has been established in the literature under suitable conditions which are not fulfilled in the case of heavy-tailed distributions. We thus focus on this framework and propose a reduced-bias approach for the classical estimators. A small simulation study is proposed to illustrate the efficiency of our approach.

Suggested Citation

  • Deme, El Hadji & Girard, Stéphane & Guillou, Armelle, 2013. "Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 550-559.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:550-559
    DOI: 10.1016/j.insmatheco.2013.03.010
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Vandewalle, B. & Beirlant, J., 2006. "On univariate extreme value statistics and the estimation of reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 441-459, June.
    4. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
    5. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    6. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    7. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
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    Cited by:

    1. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Portfolio risk analysis of excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 91-110.
    2. El Methni, Jonathan & Stupfler, Gilles, 2018. "Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions," Econometrics and Statistics, Elsevier, vol. 6(C), pages 129-148.
    3. Rassoul, Abdelaziz, 2013. "Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 698-703.
    4. Benkhelifa, Lazhar, 2014. "Kernel-type estimator of the reinsurance premium for heavy-tailed loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 65-70.

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