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Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime

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  • Brahimi, Brahim
  • Abdelli, Jihane

Abstract

Estimating the distorted parameter in the case of non negative heavy-tailed losses has been treated in Brahimi et al. (2011). In this paper, we extend this work to the case of the real heavy-tailed losses. We derive an asymptotic distribution of the estimator. We construct a practically implemented confidence interval for the distortion parameter and illustrate the performance of the interval in a simulation study with application to real data.

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  • 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.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:135-143
    DOI: 10.1016/j.insmatheco.2016.06.005
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    More about this item

    Keywords

    Proportional-hazard premium; Distortion risk measure; Distortion parameter; Extreme value; Heavy tail; Risk aversion index; Lévy-stable distribution;
    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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