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Vector-valued Coherent Risk Measures

Citations

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Cited by:

  1. c{C}au{g}{i}n Ararat & Zachary Feinstein, 2019. "Set-Valued Risk Measures as Backward Stochastic Difference Inclusions and Equations," Papers 1912.06916, arXiv.org, revised Sep 2020.
  2. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
  3. Francesca Centrone & Emanuela Rosazza Gianin, 2020. "Capital Allocation For Set-Valued Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-16, February.
  4. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01467857, HAL.
  5. Davide La Torre & Marco Maggis, 2012. "A Goal Programming Model with Satisfaction Function for Risk Management and Optimal Portfolio Diversification," Papers 1201.1783, arXiv.org, revised Sep 2012.
  6. Yanhong Chen & Zachary Feinstein, 2021. "Set-Valued Dynamic Risk Measures for Processes and Vectors," Papers 2103.00905, arXiv.org, revised Nov 2021.
  7. Alexis Bogroff & Dominique Guégan, 2019. "Artificial Intelligence, Data, Ethics. An Holistic Approach for Risks and Regulation," Working Papers 2019: 19, Department of Economics, University of Venice "Ca' Foscari".
  8. Zachary Feinstein & Birgit Rudloff, 2017. "A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle," Journal of Global Optimization, Springer, vol. 68(1), pages 47-69, May.
  9. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  10. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate Extensions Of Expectiles Risk Measures," Working Papers hal-01367277, HAL.
  11. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2015. "Conditional risk measures in a bipartite market structure," Papers 1510.00616, arXiv.org.
  12. Nakano Yumiharu, 2006. "Mean-risk optimization for index tracking," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-19, July.
  13. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.
  14. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.
  15. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Post-Print halshs-01467857, HAL.
  16. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  17. Yanhong Chen & Yijun Hu, 2019. "Set-Valued Law Invariant Coherent And Convex Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-18, May.
  18. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520, arXiv.org, revised Nov 2006.
  19. Andreas H. Hamel & Birgit Rudloff & Mihaela Yankova, 2012. "Set-valued average value at risk and its computation," Papers 1202.5702, arXiv.org, revised Jan 2013.
  20. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
  21. Zachary Feinstein & Birgit Rudloff, 2012. "Multiportfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised Oct 2014.
  22. Gabriele Canna & Francesca Centrone & Emanuela Rosazza Gianin, 2021. "Capital Allocation Rules and the No-Undercut Property," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
  23. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
  24. Cascos Fernández, Ignacio & Molchanov, Ilya, 2013. "Multivariate risk measures : a constructive approach based on selections," DES - Working Papers. Statistics and Econometrics. WS ws130101, Universidad Carlos III de Madrid. Departamento de Estadística.
  25. Burren, Daniel, 2013. "Insurance demand and welfare-maximizing risk capital—Some hints for the regulator in the case of exponential preferences and exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 551-568.
  26. Xiaochuan Deng & Fei Sun, 2019. "Regulator-based risk statistics for portfolios," Papers 1904.08829, arXiv.org, revised Jun 2020.
  27. Andreas H. Hamel & Andreas Löhne, 2014. "Lagrange Duality in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 368-397, May.
  28. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Impact of Dependence on Some Multivariate Risk Indicators," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 395-427, June.
  29. Yannick Armenti & Stephane Crepey & Samuel Drapeau & Antonis Papapantoleon, 2015. "Multivariate Shortfall Risk Allocation and Systemic Risk," Papers 1507.05351, arXiv.org, revised Mar 2017.
  30. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Risk measurement of joint risk of portfolios: a liquidity shortfall aspect," Papers 2212.04848, arXiv.org, revised May 2024.
  31. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-12, July.
  32. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.
  33. Alexis Bogroff & Dominique Guegan, 2019. "Artificial Intelligence, Data, Ethics: An Holistic Approach for Risks and Regulation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02181597, HAL.
  34. Cosimo Munari, 2021. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Finance and Stochastics, Springer, vol. 25(1), pages 77-99, January.
  35. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
  36. Elena Bernardino & Thomas Laloë & Rémi Servien, 2015. "Estimating covariate functions associated to multivariate risks: a level set approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 497-526, July.
  37. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
  38. Maume-Deschamps Véronique & Said Khalil & Rullière Didier, 2017. "Multivariate extensions of expectiles risk measures," Dependence Modeling, De Gruyter, vol. 5(1), pages 20-44, January.
  39. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
  40. Andreas H Hamel & Andreas Löhne, 2020. "Choosing sets: preface to the special issue on set optimization and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 1-4, February.
  41. Elisa Mastrogiacomo & Matteo Rocca, 2021. "Set optimization of set-valued risk measures," Annals of Operations Research, Springer, vol. 296(1), pages 291-314, January.
  42. Faugeras, Olivier & Rüschendorf, Ludger, 2018. "Risk excess measures induced by hemi-metrics," TSE Working Papers 18-922, Toulouse School of Economics (TSE).
  43. Çağin Ararat & Andreas H. Hamel & Birgit Rudloff, 2017. "Set-Valued Shortfall And Divergence Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-48, August.
  44. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
  45. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  46. Yannick Armenti & Stéphane Crépey & Samuel Drapeau & Antonis Papapantoleon, 2018. "Multivariate Shortfall Risk Allocation and Systemic Risk," Working Papers hal-01764398, HAL.
  47. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
  48. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
  49. repec:dau:papers:123456789/2278 is not listed on IDEAS
  50. c{C}au{g}{i}n Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org, revised Sep 2017.
  51. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
  52. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
  53. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
  54. Elena Di Bernardino & Clémentine Prieur, 2014. "Estimation of multivariate conditional-tail-expectation using Kendall's process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 241-267, June.
  55. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
  56. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
  57. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  58. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
  59. repec:hal:wpaper:hal-01171395 is not listed on IDEAS
  60. Zachary Feinstein & Birgit Rudloff, 2013. "Time consistency of dynamic risk measures in markets with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1473-1489, September.
  61. Cameron A. MacKenzie, 2014. "Summarizing Risk Using Risk Measures and Risk Indices," Risk Analysis, John Wiley & Sons, vol. 34(12), pages 2143-2162, December.
  62. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
  63. Maria Arduca & Pablo Koch-Medina & Cosimo Munari, 2019. "Dual representations for systemic risk measures based on acceptance sets," Papers 1906.10933, arXiv.org, revised Oct 2019.
  64. Wei, Linxiao & Hu, Yijun, 2014. "Coherent and convex risk measures for portfolios with applications," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 114-120.
  65. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
  66. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  67. Roozegar, Roohollah & Balakrishnan, Narayanaswamy & Jamalizadeh, Ahad, 2020. "On moments of doubly truncated multivariate normal mean–variance mixture distributions with application to multivariate tail conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
  68. Bazovkin, Pavel, 2014. "Geometrical framework for robust portfolio optimization," Discussion Papers in Econometrics and Statistics 01/14, University of Cologne, Institute of Econometrics and Statistics.
  69. Michel Baes & Cosimo Munari, 2020. "A continuous selection for optimal portfolios under convex risk measures does not always exist," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 5-23, February.
  70. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
  71. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
  72. Zachary Feinstein & Birgit Rudloff, 2015. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Finance and Stochastics, Springer, vol. 19(1), pages 67-107, January.
  73. Areski Cousin & Elena Di Bernardino, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
  74. Alexis Bogroff & Dominique Guegan, 2019. "Artificial Intelligence, Data, Ethics: An Holistic Approach for Risks and Regulation," Post-Print halshs-02181597, HAL.
  75. Chen, Yanhong & Hu, Yijun, 2017. "Set-valued risk statistics with scenario analysis," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 25-37.
  76. Gabriele Torri & Rosella Giacometti & Darinka Dentcheva & Svetlozar T. Rachev & W. Brent Lindquist, 2023. "ESG-coherent risk measures for sustainable investing," Papers 2309.05866, arXiv.org.
  77. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
  78. Cascos Fernández, Ignacio, 2006. "The expected convex hull trimmed regions of a sample," DES - Working Papers. Statistics and Econometrics. WS ws066919, Universidad Carlos III de Madrid. Departamento de Estadística.
  79. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
  80. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.
  81. Shushi, Tomer, 2018. "Stein’s lemma for truncated elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 297-303.
  82. Cascos Fernández, Ignacio & Molchanov, Ilya, 2006. "Multivariate risks and depth-trimmed regions," DES - Working Papers. Statistics and Econometrics. WS ws063815, Universidad Carlos III de Madrid. Departamento de Estadística.
  83. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Multivariate tail conditional expectation for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 216-223.
  84. Christoph Frei, 2020. "A New Approach to Risk Attribution and Its Application in Credit Risk Analysis," Risks, MDPI, vol. 8(2), pages 1-13, June.
  85. Hernández, Camilo, 2023. "On quadratic multidimensional type-I BSVIEs, infinite families of BSDEs and their applications," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 249-298.
  86. Bingchu Nie & Dejian Tian & Long Jiang, 2024. "Set-valued Star-Shaped Risk Measures," Papers 2402.18014, arXiv.org.
  87. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
  88. Di Bernardino, E. & Fernández-Ponce, J.M. & Palacios-Rodríguez, F. & Rodríguez-Griñolo, M.R., 2015. "On multivariate extensions of the conditional Value-at-Risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 1-16.
  89. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
  90. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  91. Hélène Cossette & Mélina Mailhot & Étienne Marceau & Mhamed Mesfioui, 2016. "Vector-Valued Tail Value-at-Risk and Capital Allocation," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 653-674, September.
  92. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Jan 2015.
  93. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2018.
  94. Imen Bentahar, 2006. "Tail Conditional Expectation for vector-valued Risks," SFB 649 Discussion Papers SFB649DP2006-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  95. Daniel Lacker, 2015. "Liquidity, risk measures, and concentration of measure," Papers 1510.07033, arXiv.org, revised Oct 2015.
  96. Balbás, Alejandro & Jiménez Guerra, Pedro, 2006. "Generalized vector risk functions," DEE - Working Papers. Business Economics. WB wb066721, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  97. Shushi, Tomer & Yao, Jing, 2020. "Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 178-186.
  98. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
  99. Andreas H. Hamel & Frank Heyde, 2021. "Set-Valued T -Translative Functions and Their Applications in Finance," Mathematics, MDPI, vol. 9(18), pages 1-33, September.
  100. Xiao Liu & Simge Küçükyavuz & Nilay Noyan, 2017. "Robust multicriteria risk-averse stochastic programming models," Annals of Operations Research, Springer, vol. 259(1), pages 259-294, December.
  101. Ekeland Ivar & Schachermayer Walter, 2011. "Law invariant risk measures on L∞ (ℝd)," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 195-225, September.
  102. repec:cte:idrepe:27672 is not listed on IDEAS
  103. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.
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