1,149
Views
4
CrossRef citations to date
0
Altmetric
Theory and Methods

Extreme and Inference for Tail Gini Functionals With Applications in Tail Risk Measurement

&
Pages 1428-1443 | Received 27 Jul 2019, Accepted 05 Feb 2020, Published online: 30 Mar 2020

References

  • Acharya, V. V. , Pedersen, L. H. , Philippon, T. , and Richardson, M. (2017), “Measuring Systemic Risk,” The Review of Financial Studies , 30, 2–47. DOI: 10.1093/rfs/hhw088.
  • Adrian, T. , and Brunnermeier, M. K. (2016), “CoVaR,” American Economic Review , 106, 1705–1741. DOI: 10.1257/aer.20120555.
  • Agarwal, V. , Ruenzi, S. , and Weigert, F. (2017), “Tail Risk in Hedge Funds: A Unique View From Portfolio Holdings,” Journal of Financial Economics , 125, 610–636. DOI: 10.1016/j.jfineco.2017.06.006.
  • Almeida, C. , Ardison, K. , Garcia, R. , and Vicente, J. (2017), “Nonparametric Tail Risk, Stock Returns, and the Macroeconomy,” Journal of Financial Econometrics , 15, 333–376. DOI: 10.1093/jjfinec/nbx007.
  • Allen, L. , Bali, T. G. , and Tang, Y. (2012), “Does Systemic Risk in the Financial Sector Predict Future Economic Downturns?,” The Review of Financial Studies , 25, 3000–3036. DOI: 10.1093/rfs/hhs094.
  • Artzner, P. , Delbaen, F. , Eber, J. M. , and Heath, D. (1999), “Coherent Measures of Risk,” Mathematical Finance , 9, 203–228. DOI: 10.1111/1467-9965.00068.
  • Asimit, A. V. , and Li, J. (2016), “Extremes for Coherent Risk Measures,” Insurance: Mathematics and Economics , 71, 332–341. DOI: 10.1016/j.insmatheco.2016.10.003.
  • Billio, M. , Getmansky, M. , Lo., A. W. , and Pelizzon, L. (2012), “Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors,” Journal of Financial Economics , 104, 535–559. DOI: 10.1016/j.jfineco.2011.12.010.
  • Brownlees, C. , and Engle, R. F. (2016), “SRISK: A Conditional Capital Shortfall Measure of Systemic Risk,” The Review of Financial Studies , 30, 48–79. DOI: 10.1093/rfs/hhw060.
  • Cai, J. J. , Chavez-Demoulin, V. , and Guillou, A. (2017), “Modified Marginal Expected Shortfall Under Asymptotic Dependence,” Biometrika , 104, 243–249. DOI: 10.1093/biomet/asx005.
  • Cai, J. J. , Einmahl, J. H. , Haan, L. , and Zhou, C. (2015), “Estimation of the Marginal Expected Shortfall: The Mean When a Related Variable Is Extreme,” Journal of the Royal Statistical Society, Series B, 77, 417–442. DOI: 10.1111/rssb.12069.
  • Ceriani, L. , and Verme, P. (2012), “The Origins of the Gini Index: Extracts From Variabilitàe Mutabilità (1912) by Corrado Gini,” The Journal of Economic Inequality , 10, 421–443. DOI: 10.1007/s10888-011-9188-x.
  • Cheng, S. , and Peng, L. (2001), “Confidence Intervals for the Tail Index,” Bernoulli , 7, 751–760. DOI: 10.2307/3318540.
  • de Haan, L. , and Ferreira, A. (2006), Extreme Value Theory: An Introduction , New York: Springer.
  • Denneberg, D. (1990), “Premium Calculation: Why Standard Deviation Should Be Replaced by Absolute Deviation,” ASTIN Bulletin: The Journal of the IAA , 20, 181–190. DOI: 10.2143/AST.20.2.2005441.
  • Fei, J. C. , Ranis, G. , and Kuo, S. W. (1978), “Growth and the Family Distribution of Income by Factor Components,” The Quarterly Journal of Economics , 92, 17–53. DOI: 10.2307/1885997.
  • Frees, E. W. , Meyers, G. , and Cummings, A. D. (2011), “Summarizing Insurance Scores Using a Gini Index,” Journal of the American Statistical Association , 106, 1085–1098. DOI: 10.1198/jasa.2011.tm10506.
  • Frees, E. W. , Meyers, G. , and Cummings, A. D. (2014), “Insurance Ratemaking and a Gini Index,” Journal of Risk and Insurance , 81, 335–366.
  • Furman, E. , and Landsman, Z. (2006), “Tail Variance Premium With Applications for Elliptical Portfolio of Risks,” ASTIN Bulletin: The Journal of the IAA , 36, 433–462. DOI: 10.1017/S0515036100014586.
  • Furman, E. , Wang, R. , and Zitikis, R. (2017), “Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks,” Journal of Banking & Finance , 83, 70–84. DOI: 10.1016/j.jbankfin.2017.06.013.
  • Gini, C. (1909), “Il Diverso Accrescimento delle Classi Sociali e la Concentrazione della Ricchezza,” Giornale degli Economisti , 38, 27–83.
  • Gini, C. (1912), Variabilità e mutabilità : Contributo allo studio delle distribuzioni e delle relazioni statistiche (Vol. III,Part II), Bologna: Cuppini.
  • Gini, C. (1914), “Sulla Misura della Concentrazione e della Variabilità dei Caratteri,” Atti del Reale Istituto veneto di scienze , lettere ed arti , 73, 1203–1248.
  • Giorgi, G. M. (1990), “Bibliographic Portrait of the Gini Concentration Ratio,” Metron , 48, 183–221.
  • Giorgi, G. M. (1993), “A Fresh Look at the Topical Interest,” Metron , 51, 83–98.
  • Giorgi, G. M. , and Gigliarano, C. (2017), “The Gini Concentration Index: A Review of the Inference Literature,” Journal of Economic Surveys , 31, 1130–1148. DOI: 10.1111/joes.12185.
  • He, Y. , Hou, Y. , and Peng, L. (2019), “Statistical Inference for a Relative Risk Measure,” Journal of Business & Economic Statistics , 37, 301–311. DOI: 10.1080/07350015.2017.1321549.
  • Kelly, B. , and Jiang, H. (2014), “Tail Risk and Asset Prices,” The Review of Financial Studies , 27, 2841–2871. DOI: 10.1093/rfs/hhu039.
  • Lerman, R. I. , and Yitzhaki, S. (1984), “A Note on the Calculation and Interpretation of the Gini Index,” Economics Letters , 15, 363–368. DOI: 10.1016/0165-1765(84)90126-5.
  • Markowitz, H. (1952), “Portfolio Selection,” The Journal of Finance , 7, 77–91. DOI: 10.2307/2975974.
  • McNeil, A. J. , Frey, R. , and Embrechts, P. (2015), Quantitative Risk Management: Concepts, Techniques and Tools (revised edition), Princeton, NJ: Princeton University Press.
  • Nelsen, R. B. (2007), An Introduction to Copulas , New York: Springer.
  • Rockafellar, R. T. , Uryasev, S. , and Zabarankin, M. (2006), “Generalized Deviations in Risk Analysis,” Finance and Stochastics , 10, 51–74. DOI: 10.1007/s00780-005-0165-8.
  • Schechtman, E. , and Yitzhaki, S. (1987), “A Measure of Association Based on Gini’s Mean Difference,” Communications in Statistics—Theory and Methods , 16, 207–231. DOI: 10.1080/03610928708829359.
  • Schechtman, E. , and Yitzhaki, S. (1999), “On the Proper Bounds of the Gini Correlation,” Economics Letters , 63, 133–138.
  • Stuart, A. (1954), “The Correlation Between Variate-Values and Ranks in Samples From a Continuous Distribution,” British Journal of Statistical Psychology , 7, 37–44. DOI: 10.1111/j.2044-8317.1954.tb00138.x.
  • Van Oordt, M. R. , and Zhou, C. (2016), “Systematic Tail Risk,” Journal of Financial and Quantitative Analysis , 51, 685–705. DOI: 10.1017/S0022109016000193.
  • Yitzhaki, S. , and Schechtman, E. (2012), The Gini Methodology: A Primer on a Statistical Methodology (Vol. 272), New York: Springer.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.