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

• Autorzy: Gzyl, Henryk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quantiles as best predictors; value at risk; tail value at risk; prediction in non-Euclidean metrics

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2024
• Tom: Vol. 44, Fasc. 1
• Strony: 15--28
• Opis fizyczny: Bibliogr. 12.poz., tab.

Twórcy

autor

Gzyl, Henryk

• IESA School of Business Caracas, Venezuela,

Bibliografia

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• [2] C. E. Bonferroni, La media esponenziale in matematica finanziaria, Annuario del Regio Istituto Superiore di Scienze Economiche e Commerciali di Bari 1923-1924, 1-14.
• [3] M. de Carvalho, Mean, what do you mean?, Amer. Statist. 70 (2016), 270-274.
• [4] B. de Finetti, Sul concetto di media, Giornale dell’Istituto Italiano degli Attuari 2 (1931), 369-396.
• [5] L. Eeckhoudt, C. Gollir, and H. Schlesinger, Economic and Financial Decisions under Risk, Princeton Univ. Press, Princeton, NJ, 2005.
• [6] M. Emery and G. Mokobodzki, Sur le barycentre d’une probabilit´e dans une vari´et´e, in: Séminaire de Probabilités XXV, Lecture Notes in Math. 1485, Springer, Berlin, 1991, 220-233.
• [7] T. Gneiting, Quantiles as optimal point predictors, Int. J. Forecasting 27 (2009), 197-207.
• [8] H. Gzyl, Prediction in Riemannian metrics derived from divergence functions, Comm. Statist. Theory Methods 51 (2022), 552-568.
• [9] R. Koenker and G. Basset Jr., Regression quantiles, Econometrica 46 (1978), 33-50.
• [10] A. J. McNeil, R. Frey, and P. Embrechts, Quantitative Risk Analysis, Princeton Univ. Press, Princeton, NJ, 2005.
• [11] J. Jacod and P. Protter, Probability Essentials, Springer, Berlin, 2000.
• [12] J. M. Oller and J. M. Corcuera, Intrinsic analysis of statistical estimation, Ann. Statist. 23 (1995), 1562-1581.

Identyfikatory

DOI

10.37190/0208-4147.00139