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Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses

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  • Brahimi, Brahim
  • Meraghni, Djamel
  • Necir, Abdelhakim
  • Zitikis, Ričardas

Abstract

The distortion parameter reflects the amount of loading in insurance premiums. A specific value of a given premium determines a value of the distortion parameter, which depends on the underlying loss distribution. Estimating the parameter, therefore, becomes a statistical inferential problem, which has been initiated by Jones and Zitikis [Jones, B.L., Zitikis, R., 2007. Risk measures, distortion parameters, and their empirical estimation. Insurance: Mathematics and Economics, 41, 279–297] in the case of the distortion premium and tackled within the framework of the central limit theorem. Heavy-tailed losses do not fall into this framework as they rely on the extreme-value theory. In this paper, we concentrate on a special but important distortion premium, called the proportional-hazard premium, and propose an estimator for its distortion parameter in the case of heavy-tailed losses. We derive an asymptotic distribution of the estimator, construct a practically implementable confidence interval for the distortion parameter, and illustrate the performance of the interval in a simulation study.

Suggested Citation

  • Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:325-334
    DOI: 10.1016/j.insmatheco.2011.05.001
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    References listed on IDEAS

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    Cited by:

    1. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 10-18.
    2. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    3. Brahimi, Brahim & Abdelli, Jihane, 2016. "Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 135-143.
    4. Vasiliy A. Anikin & Yulia P. Lezhnina & Svetlana V. Mareeva & Ekaterina D. Slobodenyuk & Nataliya N. Tikhonovà, 2016. "Income Stratification: Key Approaches and Their Application to Russia," HSE Working papers WP BRP 02/PSP/2016, National Research University Higher School of Economics.

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    More about this item

    Keywords

    Proportional-hazard premium; Proportional-hazard transform; Distortion risk measure; Distortion parameter; Extreme value; Heavy tail; Risk aversion index;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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