Assessing the difference between integrated quantiles and integrated cumulative distribution functions

Yunran Wei and Ričardas Zitikis

Insurance: Mathematics and Economics, 2023, vol. 111, issue C, 163-172

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.

Keywords: Quantile; Value-at-Risk; Integrated Value-at-Risk; Expected Shortfall; Model uncertainty; Model misspecification; Statistical inference (search for similar items in EconPapers)
JEL-codes: C02 C18 C52 D81 G22 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:111:y:2023:i:c:p:163-172

DOI: 10.1016/j.insmatheco.2023.04.002

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