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Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants

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  • Gribkova, N.V.
  • Su, J.
  • Zitikis, R.

Abstract

We derive consistency, asymptotic normality, and standard error estimation for the tail conditional allocation, also known as the marginal expected shortfall, under minimal conditions and thus geared toward widest applicability. These advances have become possible due to a newly developed technique that hinges on compound sums of concomitants. An insurance inspired numerical study has been designed to illustrate the performance of the obtained results.

Suggested Citation

  • Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:199-222
    DOI: 10.1016/j.insmatheco.2022.08.009
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    References listed on IDEAS

    as
    1. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    2. Juan-Juan Cai & John H. J. Einmahl & Laurens Haan & Chen Zhou, 2015. "Estimation of the marginal expected shortfall: the mean when a related variable is extreme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 417-442, March.
    3. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2017. "Measuring Systemic Risk," The Review of Financial Studies, Society for Financial Studies, vol. 30(1), pages 2-47.
    4. Juan‐Juan Cai & Eni Musta, 2020. "Estimation of the marginal expected shortfall under asymptotic independence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 56-83, March.
    5. N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    6. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    7. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.
    8. Denisa Banulescu-Radu & Christophe Hurlin & Jérémy Leymarie & Olivier Scaillet, 2021. "Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures," Management Science, INFORMS, vol. 67(9), pages 5730-5754, September.
    9. Hua, Lei & Joe, Harry, 2012. "Tail Comonotonicity and Conservative Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 601-629, November.
    10. Marcel Carcea & Robert Serfling, 2015. "A Gini Autocovariance Function for Time Series Modelling," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 817-838, November.
    11. Schechtman, Edna & Shelef, Amit & Yitzhaki, Shlomo & Zitikis, Ričardas, 2008. "Testing Hypotheses About Absolute Concentration Curves And Marginal Conditional Stochastic Dominance," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1044-1062, August.
    12. Nawaf Mohammed & Edward Furman & Jianxi Su, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation," Papers 2102.05003, arXiv.org, revised Aug 2021.
    13. Wang, Qiuqi & Wang, Ruodu & Zitikis, Ričardas, 2022. "Risk measures induced by efficient insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 56-65.
    14. Su, Jianxi & Furman, Edward, 2017. "A Form Of Multivariate Pareto Distribution With Applications To Financial Risk Measurement," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 331-357, January.
    15. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    16. Cossette, Hélène & Mailhot, Mélina & Marceau, Étienne, 2012. "TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 247-256.
    17. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.
    18. Christopher P. Chambers, 2009. "An Axiomatization Of Quantiles On The Domain Of Distribution Functions," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 335-342, April.
    19. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    20. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    21. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    22. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    23. Vali Asimit & Liang Peng & Ruodu Wang & Alex Yu, 2019. "An efficient approach to quantile capital allocation and sensitivity analysis," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1131-1156, October.
    24. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    25. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    26. Yeh, Hsiaw-Chan, 2004. "Some properties and characterizations for generalized multivariate Pareto distributions," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 47-60, January.
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    Cited by:

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    4. Aigner, Philipp & Schlütter, Sebastian, 2023. "Enhancing gradient capital allocation with orthogonal convexity scenarios," ICIR Working Paper Series 47/23, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).

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    More about this item

    Keywords

    Capital allocations; Marginal expected shortfall; Compound sums; Order statistics; Concomitants;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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