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Assessing the difference between integrated quantiles and integrated cumulative distribution functions

Author

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  • Wei, Yunran
  • Zitikis, Ričardas

Abstract

This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various perspectives. The invention helps to avoid a number of technical assumptions that have been traditionally imposed when working with quantities containing quantiles. In particular it helps to completely avoid the requirement of the existence of a probability density function. The developed results explain and illustrate the invention, whose byproducts include the assessment of model uncertainty and misspecification, and the derivation of statistical inference results.

Suggested Citation

  • Wei, Yunran & Zitikis, Ričardas, 2023. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 163-172.
    • Handle: RePEc:eee:insuma:v:111:y:2023:i:c:p:163-172
    DOI: 10.1016/j.insmatheco.2023.04.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Quantile; Value-at-Risk; Integrated Value-at-Risk; Expected Shortfall; Model uncertainty; Model misspecification; Statistical inference;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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