Assessing the Difference between Integrated Quantiles and Integrated Cumulative Distribution Functions

26 Pages Posted: 5 Nov 2022 Last revised: 14 Jun 2023

See all articles by Yunran Wei

Yunran Wei

University of Waterloo - Department of Statistics and Actuarial Science

Ricardas Zitikis

Western University

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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

Suggested Citation

Wei, Yunran and Zitikis, Ricardas, Assessing the Difference between Integrated Quantiles and Integrated Cumulative Distribution Functions. Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=4269014 or http://dx.doi.org/10.2139/ssrn.4269014

Yunran Wei (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Ricardas Zitikis

Western University ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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