Fadina, Tolulope and Liu, Peng and Wang, Ruodu (2023) One axiom to rule them all: A minimalist axiomatization of quantiles. SIAM Journal on Financial Mathematics, 14 (2). pp. 644-662. DOI https://doi.org/10.1137/22M1531567
Fadina, Tolulope and Liu, Peng and Wang, Ruodu (2023) One axiom to rule them all: A minimalist axiomatization of quantiles. SIAM Journal on Financial Mathematics, 14 (2). pp. 644-662. DOI https://doi.org/10.1137/22M1531567
Fadina, Tolulope and Liu, Peng and Wang, Ruodu (2023) One axiom to rule them all: A minimalist axiomatization of quantiles. SIAM Journal on Financial Mathematics, 14 (2). pp. 644-662. DOI https://doi.org/10.1137/22M1531567
Abstract
We offer a minimalist axiomatization of quantiles among all real-valued mappings on a general set of distributions through only one axiom. This axiom is called ordinality: Quantiles are the only mappings that commute with all increasing and continuous transforms. Other convenient properties of quantiles—monotonicity, semicontinuity, comonotonic additivity, elicitability, and locality in particular—follow from this axiom. Furthermore, on the set of convexly supported distributions, the median is the only mapping that commutates with all monotone and continuous transforms. On a general set of distributions, the median interval is pinned down as the unique minimal interval-valued mapping that commutes with all monotone and continuous transforms. Finally, our main result, put in a decision-theoretic setting, leads to a minimalist axiomatization of quantile preferences. In banking and insurance, quantiles are known as the standard regulatory risk measure Value-at-Risk (VaR), and thus an axiomatization of VaR is obtained with only one axiom among law-based risk measures.
Item Type: | Article |
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Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 16 Jun 2023 11:25 |
Last Modified: | 16 May 2024 21:34 |
URI: | http://repository.essex.ac.uk/id/eprint/33925 |
Available files
Filename: 2023Fadina-Liu-Wang-SIFIN.pdf
Filename: quantile axiomatics.pdf