Short communication: An axiomatization of $\Lambda$Quantiles
Bellini, F. and Peri, Ilaria (2022) Short communication: An axiomatization of $\Lambda$Quantiles. SIAM Journal on Financial Mathematics 13 (1), SC26SC38. ISSN 1945497X.

Text
Lambdaquantiles_arXiv_final.pdf  Author's Accepted Manuscript Download (270kB)  Preview 
Abstract
We give an axiomatic foundation to $\Lambda$quantiles, a family of generalized quantiles introduced in [M. Frittelli, M. Maggis, and I. Peri, Math. Finance, 24 (2014), pp. 442463] under the name Lambda Value at Risk. Under mild assumptions, we show that these functionals are characterized by a property that we call “locality,” which means that any change in the distribution of the probability mass that arises entirely above or below the value of the $\Lambda$quantile does not modify its value. We make comparisons with a related axiomatization of the usual quantiles given by Chambers in [Math. Finance, 19 (2009), pp. 335342], based on the stronger property of “ordinal covariance,” meaning that quantiles are covariant with respect to increasing transformations. Further, we present a systematic treatment of the properties of $\Lambda$quantiles, refining some of the results of Frittelli, Maggis, and Peri and [M. Burzoni, I. Peri, and C. M. Ruffo, Quant. Finance, 17 (2017), pp. 17351743] and showing that in the case of a nonincreasing $\Lambda$ the properties of $\Lambda$quantiles closely resemble those of the usual quantiles.
Metadata
Item Type:  Article 

School:  School of Business, Economics & Informatics > Economics, Mathematics and Statistics 
Depositing User:  Ilaria Peri 
Date Deposited:  25 Jan 2022 18:01 
Last Modified:  13 Jun 2022 15:16 
URI:  https://eprints.bbk.ac.uk/id/eprint/47295 
Statistics
Additional statistics are available via IRStats2.