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Extreme-aggregation measures in the RDEU model

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  • Chen, Ouxiang
  • Hu, Taizhong

Abstract

In order to characterize the most superadditive behavior of a risk measure, the notion of extreme-aggregation risk measures was introduced in the literature. In this short note, explicit forms of the extreme-aggregation measures induced by rank-dependent expected utility (RDEU) functionals and by RDEU-based shortfall risk measures are derived. The main results generalize those known in the literature.

Suggested Citation

  • Chen, Ouxiang & Hu, Taizhong, 2019. "Extreme-aggregation measures in the RDEU model," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 155-163.
    • Handle: RePEc:eee:stapro:v:148:y:2019:i:c:p:155-163
    DOI: 10.1016/j.spl.2019.01.023
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    References listed on IDEAS

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    1. Niushan Gao & Cosimo Munari, 2017. "Surplus-invariant risk measures," Papers 1707.04949, arXiv.org, revised May 2018.
    2. 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.
    3. Ruodu Wang, 2016. "Regulatory arbitrage of risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 337-347, March.
    4. 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.
    5. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    8. Jun Cai & Haiyan Liu & Ruodu Wang, 2018. "Asymptotic Equivalence Of Risk Measures Under Dependence Uncertainty," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 29-49, January.
    9. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    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. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    12. 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.
    13. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    14. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.

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