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On optimal portfolio diversification with respect to extreme risks

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  • Georg Mainik
  • Ludger Rüschendorf

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Suggested Citation

  • Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
  • Handle: RePEc:spr:finsto:v:14:y:2010:i:4:p:593-623
    DOI: 10.1007/s00780-010-0122-z
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    References listed on IDEAS

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    1. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non‐parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 307-335, June.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. Einmahl, John H.J. & de Haan, Laurens & Sinha, Ashoke Kumar, 1997. "Estimating the spectral measure of an extreme value distribution," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 143-171, October.
    4. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    5. Einmahl, J.H.J. & de Haan, L.F.M. & Piterbarg, V.I., 2001. "Nonparametric estimation of the spectral measure of an extreme value distribution," Other publications TiSEM c3485b9b-a0bd-456f-9baa-0, Tilburg University, School of Economics and Management.
    6. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    7. H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
    8. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
    9. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
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    Citations

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    Cited by:

    1. Einmahl, John & Yang, Fan & Zhou, Chen, 2018. "Testing the Multivariate Regular Variation Model," Discussion Paper 2018-044, Tilburg University, Center for Economic Research.
    2. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.
    3. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    4. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    5. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    6. Kley, Oliver & Klüppelberg, Claudia & Paterlini, Sandra, 2020. "Modelling extremal dependence for operational risk by a bipartite graph," Journal of Banking & Finance, Elsevier, vol. 117(C).
    7. Tong, Bin & Wu, Chongfeng & Xu, Weidong, 2012. "Risk concentration of aggregated dependent risks: The second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 139-149.
    8. Peter Tankov, 2014. "Tails of weakly dependent random vectors," Papers 1402.4683, arXiv.org, revised Jan 2016.
    9. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.
    10. Shi, Xiaojun & Tang, Qihe & Yuan, Zhongyi, 2017. "A limit distribution of credit portfolio losses with low default probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 156-167.
    11. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias, 2015. "A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-14, October.
    12. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.
    13. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    14. Konstantinides, Dimitrios G. & Li, Jinzhu, 2016. "Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 38-44.
    15. Oliver Kley & Claudia Klüppelberg & Sandra Paterlini, 2019. "Modelling Extremal Dependence for Operational Risk by a Bipartite Graph," DEM Working Papers 2019/2, Department of Economics and Management.
    16. Anand Deo & Karthyek Murthy, 2020. "Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives," Papers 2008.09818, arXiv.org.
    17. Oliver Kley & Claudia Kluppelberg & Sandra Paterlini, 2019. "Modelling Extremal Dependence for Operational Risk by a Bipartite Graph," Papers 1902.03041, arXiv.org.
    18. Li, Jinzhu, 2016. "Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 195-204.
    19. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    20. Moosup Kim & Sangyeol Lee, 2017. "Estimation of the tail exponent of multivariate regular variation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 945-968, October.

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    More about this item

    Keywords

    Portfolio optimization; Risk management; Diversification effects; Multivariate extremes; 62G32; 62G05; 62G20; 62P05; C13; C14; G11;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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