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Monotone and cash-invariant convex functions and hulls

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  • Filipovic, Damir
  • Kupper, Michael

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  • Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    • Handle: RePEc:eee:insuma:v:41:y:2007:i:1:p:1-16
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    1. 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.
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    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    6. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    7. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    8. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    9. Bühlmann, Hans, 1984. "The General Economic Premium Principle," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 13-21, April.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172, April.
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. 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.
    2. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    3. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    4. Marcelo Brutti Righi, 2019. "A composition between risk and deviation measures," Annals of Operations Research, Springer, vol. 282(1), pages 299-313, November.
    5. 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.
    6. Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    7. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    8. Damir Filipović, 2008. "Optimal Numeraires For Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 333-336, April.
    9. Filipovic, Damir & Vogelpoth, Nicolas, 2008. "A note on the Swiss Solvency Test risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 897-902, June.
    10. M. Volle, 2012. "A primal–dual operation on sets linked with closed convex relaxation processes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 534-546, July.
    11. Dimitrios Konstantinides & Christos Kountzakis, 2014. "The restricted convex risk measures in actuarial solvency," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 287-318, October.
    12. Radu Boţ & Alina-Ramona Frătean, 2011. "Looking for appropriate qualification conditions for subdifferential formulae and dual representations for convex risk measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 191-215, October.
    13. Mao, Tiantian & Hu, Jiuyun & Liu, Haiyan, 2018. "The average risk sharing problem under risk measure and expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 170-179.
    14. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    15. 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.
    16. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Beyond cash-additive risk measures: when changing the num\'{e}raire fails," Papers 1206.0478, arXiv.org, revised Feb 2014.
    17. 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.
    18. Alev{s} v{C}ern'y, 2020. "The Hansen ratio in mean--variance portfolio theory," Papers 2007.15980, arXiv.org.
    19. Karl-Theodor Eisele & Philippe Artzner, 2013. "Multiperiod Banking Supervision," Working Papers of LaRGE Research Center 2013-05, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    20. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    21. Marcelo Brutti Righi, 2015. "A composition between risk and deviation measures," Papers 1511.06943, arXiv.org, revised May 2018.
    22. Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised Feb 2024.
    23. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.

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