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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 44, Fasc. 1,
pages 15 - 28
DOI: 10.37190/0208-4147.00139
Published online 10.6.2024
 

A predictive approach to quantiles: Application to Value at Risk and Tail Value at Risk

Henryk Gzyl

Abstract:

We prove that quantiles are best predictors in a special metric. The best predictor turns out to coincide with the notions of generalized arithmetic mean, exponential barycenter and certainty equivalent. We also show that the computation of tail value at risk (TVaR) reduces to the computation of a quantile with a higher level of confidence. This point of view makes the analysis of the statistical properties of TVaR easier.

2010 AMS Mathematics Subject Classification: Primary 60A99; Secondary 60D99, 62G08.

Keywords and phrases: quantiles as best predictors, value at risk, tail value at risk, prediction in non-Euclidean metrics.

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