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A Representation Result For Concave Schur Concave Functions

Citations

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Cited by:

  1. Nilay Noyan & Gábor Rudolf, 2015. "Kusuoka representations of coherent risk measures in general probability spaces," Annals of Operations Research, Springer, vol. 229(1), pages 591-605, June.
  2. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
  3. repec:dau:papers:123456789/2348 is not listed on IDEAS
  4. Bogdan Grechuk & Michael Zabarankin, 2012. "Optimal risk sharing with general deviation measures," Annals of Operations Research, Springer, vol. 200(1), pages 9-21, November.
  5. M. Kaina & L. Rüschendorf, 2009. "On convex risk measures on L p -spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 475-495, July.
  6. Pflug Georg Ch., 2006. "On distortion functionals," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-16, July.
  7. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  8. Berkhouch, Mohammed & Lakhnati, Ghizlane, 2017. "Extended Gini-type measures of risk and variability," MPRA Paper 80329, University Library of Munich, Germany.
  9. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
  10. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
  11. Mohammed Berkhouch & Ghizlane Lakhnati & Marcelo Brutti Righi, 2017. "Extended Gini-type measures of risk and variability," Papers 1707.07322, arXiv.org, revised Mar 2018.
  12. Laeven, R.J.A. & Stadje, M.A., 2011. "Entropy Coherent and Entropy Convex Measures of Risk," Discussion Paper 2011-031, Tilburg University, Center for Economic Research.
  13. Ghossoub, Mario, 2015. "Vigilant measures of risk and the demand for contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 27-35.
  14. Alois Pichler, 2013. "Premiums And Reserves, Adjusted By Distortions," Papers 1304.0490, arXiv.org.
  15. Ruodu Wang & Yunran Wei & Gordon E. Willmot, 2020. "Characterization, Robustness, and Aggregation of Signed Choquet Integrals," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 993-1015, August.
  16. Grigorova Miryana, 2014. "Stochastic dominance with respect to a capacity and risk measures," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 1-37, December.
  17. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-12, July.
  18. Grigorova Miryana, 2014. "Stochastic orderings with respect to a capacity and an application to a financial optimization problem," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-31, June.
  19. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  20. Grechuk, Bogdan, 2015. "The center of a convex set and capital allocation," European Journal of Operational Research, Elsevier, vol. 243(2), pages 628-636.
  21. Roger J. A. Laeven & Mitja Stadje, 2013. "Entropy Coherent and Entropy Convex Measures of Risk," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 265-293, May.
  22. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
  23. Rose-Anne Dana, 2011. "Comonotonicity, Efficient Risk-sharing and Equilibria in markets with short-selling for concave law-invariant utilities," Post-Print hal-00655172, HAL.
  24. Pichler, Alois & Shapiro, Alexander, 2015. "Minimal representation of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 184-193.
  25. Alexander Vinel & Pavlo A. Krokhmal, 2017. "Certainty equivalent measures of risk," Annals of Operations Research, Springer, vol. 249(1), pages 75-95, February.
  26. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
  27. Miryana Grigorova, 2011. "Stochastic dominance with respect to a capacity and risk measures," Working Papers hal-00639667, HAL.
  28. Grechuk, Bogdan & Zabarankin, Michael, 2014. "Inverse portfolio problem with mean-deviation model," European Journal of Operational Research, Elsevier, vol. 234(2), pages 481-490.
  29. Acciaio Beatrice & Svindland Gregor, 2013. "Are law-invariant risk functions concave on distributions?," Dependence Modeling, De Gruyter, vol. 1, pages 54-64, December.
  30. Claudia Ravanelli & Gregor Svindland, 2014. "Comonotone Pareto optimal allocations for law invariant robust utilities on L 1," Finance and Stochastics, Springer, vol. 18(1), pages 249-269, January.
  31. Alexander Shapiro, 2013. "On Kusuoka Representation of Law Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 142-152, February.
  32. Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
  33. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
  34. Svindland Gregor, 2009. "Subgradients of law-invariant convex risk measures on L," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 169-199, December.
  35. Song, Yongsheng & Yan, Jia-An, 2009. "Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 459-465, December.
  36. Dilip Madan & Martijn Pistorius & Mitja Stadje, 2013. "On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation," Papers 1301.3531, arXiv.org, revised Apr 2017.
  37. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
  38. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.
  39. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
  40. Liebrich, Felix-Benedikt & Svindland, Gregor, 2019. "Efficient allocations under law-invariance: A unifying approach," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 28-45.
  41. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-19, July.
  42. Alois Pichler & Alexander Shapiro, 2012. "Uniqueness of Kusuoka Representations," Papers 1210.7257, arXiv.org, revised Feb 2013.
  43. repec:dau:papers:123456789/2278 is not listed on IDEAS
  44. Thomas Knispel & Roger J. A. Laeven & Gregor Svindland, 2021. "Asymptotic Analysis of Risk Premia Induced by Law-Invariant Risk Measures," Papers 2107.01730, arXiv.org.
  45. Pichler, Alois, 2013. "The natural Banach space for version independent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 405-415.
  46. Bogdan Grechuk & Andrzej Palczewski & Jan Palczewski, 2018. "On the solution uniqueness in portfolio optimization and risk analysis," Papers 1810.11299, arXiv.org, revised Oct 2020.
  47. Dana, R.-A., 2011. "Comonotonicity, efficient risk-sharing and equilibria in markets with short-selling for concave law-invariant utilities," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 328-335.
  48. Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2009. "Maximum Entropy Principle with General Deviation Measures," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 445-467, May.
  49. Xia Han & Ruodu Wang & Qinyu Wu, 2023. "Monotonic mean-deviation risk measures," Papers 2312.01034, arXiv.org.
  50. Carlier Guillaume & Dana Rose-Anne, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-26, July.
  51. Carlier, G. & Dana, R.-A., 2007. "Are generalized call-spreads efficient?," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 581-596, June.
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