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Measuring and comparing risks of different types

Author

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  • Aigner, Maximilian
  • Chavez-Demoulin, Valérie
  • Guillou, Armelle

Abstract

Being able to compare risk measures in practice is crucial in many applications such as in finance, insurance or environmental science. The difficulty is that the variables of interest are not always of the same nature, nor of the same type or scale. Thus the usual risk measures are often misleading and to solve this issue we propose to use the Expected Proportional Shortfall (EPS) which is scale invariant and thus, which does not depend on the unit of measurement. To estimate the EPS, an estimator of the tail index γ is required. The main asymptotic properties of our EPS estimator are provided under very general assumptions in case of d-variate β-mixing processes with Pareto-type marginals. Then, we propose a test statistic based on the EPS estimators to compare different risks, whatever their nature/type/scale are. Since the performances of the test statistic are poor when a biased estimate of γ is used, we propose to perform our EPS estimation with an asymptotically unbiased estimator for γ. The efficiency of our test statistic is illustrated in a simulation experiment and validated on an environmental dataset.

Suggested Citation

  • Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.
    • Handle: RePEc:eee:insuma:v:102:y:2022:i:c:p:1-21
    DOI: 10.1016/j.insmatheco.2021.11.001
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    References listed on IDEAS

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    More about this item

    Keywords

    Asymptotically unbiased estimator; β-mixing; Convergence in distribution; Expected Proportional Shortfall; Hypothesis testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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