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Law Invariant Risk Measures Have the Fatou Property

Citations

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Cited by:

  1. Gilles Angelsberg & Freddy Delbaen & Ivo Kaelin & Michael Kupper & Joachim Näf, 2011. "On a class of law invariant convex risk measures," Finance and Stochastics, Springer, vol. 15(2), pages 343-363, June.
  2. 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.
  3. 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.
  4. Guangyan Jia & Jianming Xia & Rongjie Zhao, 2020. "Monetary Risk Measures," Papers 2012.06751, arXiv.org.
  5. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
  6. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
  7. Krätschmer, Volker & Zähle, Henryk, 2011. "Sensitivity of risk measures with respect to the normal approximation of total claim distributions," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 335-344.
  8. Marcelo Brutti Righi, 2019. "A composition between risk and deviation measures," Annals of Operations Research, Springer, vol. 282(1), pages 299-313, November.
  9. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  10. Kerem Ugurlu, 2014. "On the Coherent Risk Measure Representations in the Discrete Probability Spaces," Papers 1411.4441, arXiv.org, revised Dec 2014.
  11. 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.
  12. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Working Papers hal-00921283, HAL.
  13. Liu, Peng & Wang, Ruodu & Wei, Linxiao, 2020. "Is the inf-convolution of law-invariant preferences law-invariant?," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 144-154.
  14. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
  15. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
  16. 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.
  17. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
  18. Ghossoub, Mario, 2015. "Vigilant measures of risk and the demand for contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 27-35.
  19. Tolulope Fadina & Yang Liu & Ruodu Wang, 2021. "A Framework for Measures of Risk under Uncertainty," Papers 2110.10792, arXiv.org, revised Sep 2023.
  20. Alois Pichler, 2013. "Premiums And Reserves, Adjusted By Distortions," Papers 1304.0490, arXiv.org.
  21. 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.
  22. Niushan Gao & Denny H. Leung & Foivos Xanthos, 2016. "Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures," Papers 1610.08806, arXiv.org, revised Jun 2017.
  23. Schied, Alexander, 2005. "Optimal investments for risk- and ambiguity-averse preferences: A duality approach," SFB 649 Discussion Papers 2005-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  24. Niushan Gao & Foivos Xanthos, 2015. "On the C-property and $w^*$-representations of risk measures," Papers 1511.03159, arXiv.org, revised Sep 2016.
  25. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," LSE Research Online Documents on Economics 50119, London School of Economics and Political Science, LSE Library.
  26. Geissel Sebastian & Sass Jörn & Seifried Frank Thomas, 2018. "Optimal expected utility risk measures," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 73-87, January.
  27. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
  28. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, February.
  29. Niushan Gao & Denny Leung & Cosimo Munari & Foivos Xanthos, 2018. "Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces," Finance and Stochastics, Springer, vol. 22(2), pages 395-415, April.
  30. repec:hal:journl:hal-00921283 is not listed on IDEAS
  31. Christa Cuchiero & Guido Gazzani & Irene Klein, 2022. "Risk measures under model uncertainty: a Bayesian viewpoint," Papers 2204.07115, arXiv.org.
  32. Alfred Galichon, 2010. "The Var At Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 503-506.
  33. Niushan Gao & Denny H. Leung & Cosimo Munari & Foivos Xanthos, 2017. "Fatou Property, representations, and extensions of law-invariant risk measures on general Orlicz spaces," Papers 1701.05967, arXiv.org, revised Sep 2017.
  34. De Franco, Carmine & Tankov, Peter, 2011. "Portfolio insurance under a risk-measure constraint," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 361-370.
  35. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  36. Grechuk, Bogdan, 2015. "The center of a convex set and capital allocation," European Journal of Operational Research, Elsevier, vol. 243(2), pages 628-636.
  37. Bellini, Fabio & Koch-Medina, Pablo & Munari, Cosimo & Svindland, Gregor, 2021. "Law-invariant functionals that collapse to the mean," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 83-91.
  38. Tobias Fissler & Jana Hlavinov'a & Birgit Rudloff, 2019. "Elicitability and Identifiability of Systemic Risk Measures," Papers 1907.01306, arXiv.org, revised Oct 2019.
  39. Shengzhong Chen & Niushan Gao & Denny Leung & Lei Li, 2021. "Automatic Fatou Property of Law-invariant Risk Measures," Papers 2107.08109, arXiv.org, revised Jan 2022.
  40. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  41. Pablo Koch-Medina & Cosimo Munari, 2014. "Law-invariant risk measures: extension properties and qualitative robustness," Papers 1401.3121, arXiv.org.
  42. repec:hum:wpaper:sfb649dp2007-010 is not listed on IDEAS
  43. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  44. 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.
  45. Keita Owari, 2013. "On the Lebesgue Property of Monotone Convex Functions," CARF F-Series CARF-F-317, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  46. Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," Papers 1305.6023, arXiv.org, revised May 2015.
  47. Pichler, Alois & Shapiro, Alexander, 2015. "Minimal representation of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 184-193.
  48. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
  49. Qiuqi Wang & Ruodu Wang & Ricardas Zitikis, 2021. "Risk measures induced by efficient insurance contracts," Papers 2109.00314, arXiv.org, revised Sep 2021.
  50. 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.
  51. Pablo Koch-Medina & Santiago Moreno-Bromberg & Cosimo Munari, 2014. "Capital adequacy tests and limited liability of financial institutions," Papers 1401.3133, arXiv.org, revised Feb 2014.
  52. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.
  53. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
  54. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2020. "Law-invariant functionals that collapse to the mean," Papers 2009.04144, arXiv.org, revised Jan 2021.
  55. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
  56. Ruodu Wang & Johanna F. Ziegel, 2021. "Scenario-based risk evaluation," Finance and Stochastics, Springer, vol. 25(4), pages 725-756, October.
  57. Bellini, Fabio & Rosazza Gianin, Emanuela, 2008. "On Haezendonck risk measures," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 986-994, June.
  58. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
  59. Nabil Kazi-Tani, 2018. "Inf-Convolution of Choquet Integrals and Applications in Optimal Risk Transfer," Working Papers hal-01742629, HAL.
  60. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
  61. Cont Rama & Deguest Romain & He Xue Dong, 2013. "Loss-based risk measures," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 133-167, June.
  62. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
  63. Mucahit Aygun & Fabio Bellini & Roger J. A. Laeven, 2023. "Elicitability of Return Risk Measures," Papers 2302.13070, arXiv.org, revised Mar 2023.
  64. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
  65. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
  66. Acciaio Beatrice & Svindland Gregor, 2013. "Are law-invariant risk functions concave on distributions?," Dependence Modeling, De Gruyter, vol. 1(2013), pages 54-64, December.
  67. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
  68. Nendel, Max & Riedel, Frank & Schmeck, Maren Diane, 2021. "A decomposition of general premium principles into risk and deviation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 193-209.
  69. Ekeland Ivar & Schachermayer Walter, 2011. "Law invariant risk measures on L∞ (ℝd)," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 195-225, September.
  70. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Working Papers hal-00629929, HAL.
  71. Beatrice Acciaio, 2009. "Short note on inf-convolution preserving the Fatou property," Annals of Finance, Springer, vol. 5(2), pages 281-287, March.
  72. Alexander Shapiro, 2013. "On Kusuoka Representation of Law Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 142-152, February.
  73. Freddy Delbaen, 2009. "Risk Measures For Non‐Integrable Random Variables," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 329-333, April.
  74. Sarah Bensalem & Nicolás Hernández Santibáñez & Nabil Kazi-Tani, 2019. "Prevention efforts, insurance demand and price incentives under coherent risk measures," Working Papers hal-01983433, HAL.
  75. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
  76. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2024. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Annals of Operations Research, Springer, vol. 336(1), pages 829-860, May.
  77. Xue Dong He & Hanqing Jin & Xun Yu Zhou, 2015. "Dynamic Portfolio Choice When Risk Is Measured by Weighted VaR," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 773-796, March.
  78. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
  79. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
  80. Haier Andreas & Molchanov Ilya, 2019. "Multivariate risk measures in the non-convex setting," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 25-35, December.
  81. Svindland Gregor, 2009. "Subgradients of law-invariant convex risk measures on L," Statistics & Risk Modeling, De Gruyter, vol. 27(02), pages 169-199, December.
  82. Daniel Lacker, 2015. "Law invariant risk measures and information divergences," Papers 1510.07030, arXiv.org, revised Jun 2016.
  83. Shengzhong Chen & Niushan Gao & Foivos Xanthos, 2018. "The strong Fatou property of risk measures," Papers 1805.05259, arXiv.org.
  84. 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.
  85. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
  86. Takashi Kato, 2017. "Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level," Papers 1711.07335, arXiv.org.
  87. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
  88. Kiesel Swen & Rüschendorf Ludger, 2014. "Optimal risk allocation for convex risk functionals in general risk domains," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 335-365, December.
  89. Moresco, Marlon Ruoso & Righi, Marcelo Brutti, 2022. "On the link between monetary and star-shaped risk measures," Statistics & Probability Letters, Elsevier, vol. 184(C).
  90. 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.
  91. repec:dau:papers:123456789/2279 is not listed on IDEAS
  92. 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.
  93. Made Tantrawan & Denny H. Leung, 2018. "On closedness of law-invariant convex sets in rearrangement invariant spaces," Papers 1810.10374, arXiv.org, revised Dec 2019.
  94. Ludovic Tangpi, 2018. "Efficient hedging under ambiguity in continuous time," Papers 1812.10876, arXiv.org, revised Mar 2019.
  95. Alois Pichler & Alexander Shapiro, 2012. "Uniqueness of Kusuoka Representations," Papers 1210.7257, arXiv.org, revised Feb 2013.
  96. Arthur Charpentier, 2018. "An introduction to multivariate and dynamic risk measures," Working Papers hal-01831481, HAL.
  97. Bauerle, Nicole & Muller, Alfred, 2006. "Stochastic orders and risk measures: Consistency and bounds," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 132-148, February.
  98. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
  99. Daniel Bartl & Ludovic Tangpi, 2020. "Non-asymptotic convergence rates for the plug-in estimation of risk measures," Papers 2003.10479, arXiv.org, revised Oct 2022.
  100. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.
  101. Tobias Fissler & Johanna F. Ziegel, 2015. "Higher order elicitability and Osband's principle," Papers 1503.08123, arXiv.org, revised Sep 2015.
  102. Freddy Delbaen & Keita Owari, 2016. "Convex functions on dual Orlicz spaces," Papers 1611.06218, arXiv.org, revised Dec 2017.
  103. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
  104. Bensalem, Sarah & Santibáñez, Nicolás Hernández & Kazi-Tani, Nabil, 2020. "Prevention efforts, insurance demand and price incentives under coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 369-386.
  105. Georg Ch. Pflug & Alois Pichler, 2016. "Time-Consistent Decisions and Temporal Decomposition of Coherent Risk Functionals," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 682-699, May.
  106. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
  107. Ludger Rüschendorf, 2012. "Worst case portfolio vectors and diversification effects," Finance and Stochastics, Springer, vol. 16(1), pages 155-175, January.
  108. repec:dau:papers:123456789/2278 is not listed on IDEAS
  109. Martin Herdegen & Nazem Khan, 2022. "Mean‐ρ$\rho$ portfolio selection and ρ$\rho$‐arbitrage for coherent risk measures," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 226-272, January.
  110. Krätschmer, Volker, 2007. "On {sigma}-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model," SFB 649 Discussion Papers 2007-010, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  111. Jiarui Chu & Ludovic Tangpi, 2021. "Non-asymptotic estimation of risk measures using stochastic gradient Langevin dynamics," Papers 2111.12248, arXiv.org, revised Feb 2023.
  112. Koch-Medina Pablo & Munari Cosimo, 2014. "Law-invariant risk measures: Extension properties and qualitative robustness," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 215-236, December.
  113. Martin Glanzer & Georg Ch. Pflug & Alois Pichler, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709, arXiv.org, revised Jan 2019.
  114. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
  115. Pichler, Alois, 2013. "The natural Banach space for version independent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 405-415.
  116. Debora Daniela Escobar & Georg Ch. Pflug, 2020. "The distortion principle for insurance pricing: properties, identification and robustness," Annals of Operations Research, Springer, vol. 292(2), pages 771-794, September.
  117. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
  118. Andreas Haier & Ilya Molchanov, 2019. "Multivariate risk measures in the non-convex setting," Papers 1902.00766, arXiv.org, revised Sep 2019.
  119. 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.
  120. 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.
  121. Erick Delage & Daniel Kuhn & Wolfram Wiesemann, 2019. "“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?," Management Science, INFORMS, vol. 65(7), pages 3282-3301, July.
  122. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
  123. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
  124. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 426-433, June.
  125. repec:hum:wpaper:sfb649dp2005-051 is not listed on IDEAS
  126. Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.
  127. Daniel Lacker, 2015. "Liquidity, risk measures, and concentration of measure," Papers 1510.07033, arXiv.org, revised Oct 2015.
  128. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.
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