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An elementary proof of the dual representation of expected shortfall
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Herdegen, Martin and Munari, Cosimo (2023) An elementary proof of the dual representation of expected shortfall. Mathematics and Financial Economics, 17 . pp. 655-662. doi:10.1007/s11579-023-00346-8 ISSN 1862-9679.
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Official URL: https://doi.org/10.1007/s11579-023-00346-8
Abstract
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic properties of quantile functions and can thus be easily implemented in any graduate course on risk measures. As a byproduct, we obtain a new proof of the subadditivity of Expected Shortfall.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Duality theory (Mathematics), Inequalities (Mathematics), Stochastic orders | ||||||||
Journal or Publication Title: | Mathematics and Financial Economics | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 1862-9679 | ||||||||
Official Date: | December 2023 | ||||||||
Dates: |
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Volume: | 17 | ||||||||
Page Range: | pp. 655-662 | ||||||||
DOI: | 10.1007/s11579-023-00346-8 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 23 October 2023 | ||||||||
Date of first compliant Open Access: | 27 November 2023 | ||||||||
RIOXX Funder/Project Grant: |
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