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Vector-valued Coherent Risk Measures

Citations

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Cited by:

  1. 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.
  2. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  3. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Post-Print halshs-01467857, HAL.
  4. 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.
  5. 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.
  6. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
  7. Balbás, Beatriz & Balbás, Raquel, 2018. "Golden options in financial mathematics," IC3JM - Estudios = Working Papers 27672, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
  8. 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.
  9. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  10. Yannick Armenti & Stéphane Crépey & Samuel Drapeau & Antonis Papapantoleon, 2018. "Multivariate Shortfall Risk Allocation and Systemic Risk," Working Papers hal-01764398, HAL.
  11. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
  12. Philipp Kreins & Stanislaus Maier-Paape & Qiji Jim Zhu, 2024. "Quick Introduction into the General Framework of Portfolio Theory," Risks, MDPI, vol. 12(8), pages 1-24, August.
  13. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
  14. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  15. 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.
  16. 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.
  17. Wei, Linxiao & Hu, Yijun, 2014. "Coherent and convex risk measures for portfolios with applications," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 114-120.
  18. 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.
  19. 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.
  20. Chen, Yanhong & Hu, Yijun, 2017. "Set-valued risk statistics with scenario analysis," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 25-37.
  21. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.
  22. 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.
  23. 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.
  24. 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.
  25. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
  26. Ekeland Ivar & Schachermayer Walter, 2011. "Law invariant risk measures on L∞ (ℝd)," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 195-225, September.
  27. 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.
  28. Yanhong Chen & Zachary Feinstein, 2021. "Set-Valued Dynamic Risk Measures for Processes and Vectors," Papers 2103.00905, arXiv.org, revised Nov 2021.
  29. 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".
  30. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate Extensions Of Expectiles Risk Measures," Working Papers hal-01367277, HAL.
  31. 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.
  32. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  33. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520, arXiv.org, revised Nov 2006.
  34. 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.
  35. Emmanuel Lepinette & Duc Thinh Vu, 2024. "Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation," Papers 2405.06764, arXiv.org.
  36. 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.
  37. Xiaochuan Deng & Fei Sun, 2019. "Regulator-based risk statistics for portfolios," Papers 1904.08829, arXiv.org, revised Jun 2020.
  38. Yannick Armenti & Stephane Crepey & Samuel Drapeau & Antonis Papapantoleon, 2015. "Multivariate Shortfall Risk Allocation and Systemic Risk," Papers 1507.05351, arXiv.org, revised Mar 2017.
  39. 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.
  40. 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.
  41. Maume-Deschamps Véronique & Rullière Didier & Said Khalil, 2017. "Multivariate extensions of expectiles risk measures," Dependence Modeling, De Gruyter, vol. 5(1), pages 20-44, January.
  42. Elisa Mastrogiacomo & Matteo Rocca, 2021. "Set optimization of set-valued risk measures," Annals of Operations Research, Springer, vol. 296(1), pages 291-314, January.
  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. 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.
  45. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
  46. repec:dau:papers:123456789/2278 is not listed on IDEAS
  47. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  48. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
  49. 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).
  50. Alexis Bogroff & Dominique Guegan, 2019. "Artificial Intelligence, Data, Ethics: An Holistic Approach for Risks and Regulation," Post-Print halshs-02181597, HAL.
  51. 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.
  52. repec:cte:wsrepe:ws066919 is not listed on IDEAS
  53. Shushi, Tomer, 2018. "Stein’s lemma for truncated elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 297-303.
  54. 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.
  55. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2015. "Conditional risk measures in a bipartite market structure," Papers 1510.00616, arXiv.org.
  61. Zachary Feinstein & Birgit Rudloff, 2012. "Multiportfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised Oct 2014.
  62. Balbás, Raquel, 2006. "Optimizing Measures of Risk: A Simplex-like Algorithm," DEE - Working Papers. Business Economics. WB 6534, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  63. 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.
  64. 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.
  65. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-12, July.
  66. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
  67. 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.
  68. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
  69. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
  70. 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.
  71. 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.
  72. 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.
  73. 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.
  74. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
  75. 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.
  76. repec:cte:idrepe:27672 is not listed on IDEAS
  77. 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.
  78. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
  79. 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.
  80. Nakano Yumiharu, 2006. "Mean-risk optimization for index tracking," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-19, July.
  81. 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.
  82. 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.
  83. 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.
  84. 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.
  85. 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.
  86. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
  87. Faugeras, Olivier & Rüschendorf, Ludger, 2018. "Risk excess measures induced by hemi-metrics," TSE Working Papers 18-922, Toulouse School of Economics (TSE).
  88. 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.
  89. 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.
  90. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
  91. 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.
  92. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
  93. repec:hal:wpaper:hal-01171395 is not listed on IDEAS
  94. Cameron A. MacKenzie, 2014. "Summarizing Risk Using Risk Measures and Risk Indices," Risk Analysis, John Wiley & Sons, vol. 34(12), pages 2143-2162, December.
  95. 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.
  96. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  97. 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.
  98. 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.
  99. 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.
  100. Areski Cousin & Elena Di Bernardino, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
  101. 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.
  102. Bentahar, Imen, 2006. "Tail Conditional Expectation for vector-valued risks," SFB 649 Discussion Papers 2006-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  103. Bingchu Nie & Dejian Tian & Long Jiang, 2024. "Set-valued Star-Shaped Risk Measures," Papers 2402.18014, arXiv.org.
  104. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Jan 2015.
  105. repec:hum:wpaper:sfb649dp2006-029 is not listed on IDEAS
  106. Daniel Lacker, 2015. "Liquidity, risk measures, and concentration of measure," Papers 1510.07033, arXiv.org, revised Oct 2015.
  107. 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.
  108. 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.
  109. 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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