Haezendonck–Goovaerts risk measures and Orlicz quantiles
In this paper, we study the well-known Haezendonck–Goovaerts risk measures on their natural domain, that is on Orlicz spaces and, in particular, on Orlicz hearts. We provide a dual representation as well as the optimal scenario in such a representation and investigate the properties of the minimizer xα∗ (that we call Orlicz quantile) in the definition of the Haezendonck–Goovaerts risk measure. Since Orlicz quantiles fail to satisfy an internality property, bilateral Orlicz quantiles are also introduced and analyzed.
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- Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214.
- 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, 04.
- Bellini Fabio & Rosazza Gianin Emanuela, 2008. "Optimal portfolios with Haezendonck risk measures," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 89-108, March.
- 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.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275, June.
- 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.
- Chen, Zehua, 1996. "Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 107-115, August.
- Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
- Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
- 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.
- Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2004. "Some new classes of consistent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 505-516, June.
- Bellini, Fabio & Rosazza Gianin, Emanuela, 2008. "On Haezendonck risk measures," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 986-994, June.
- Denis Belomestny & Volker KrÃ¤tschmer, 2010. "Central limit theorems for law-invariant coherent risk measures," SFB 649 Discussion Papers SFB649DP2010-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Haezendonck, J. & Goovaerts, M., 1982. "A new premium calculation principle based on Orlicz norms," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 41-53, January.
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