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Asymptotic distribution of law-invariant risk functionals

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  • Georg Pflug
  • Nancy Wozabal

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  • Georg Pflug & Nancy Wozabal, 2010. "Asymptotic distribution of law-invariant risk functionals," Finance and Stochastics, Springer, vol. 14(3), pages 397-418, September.
    • Handle: RePEc:spr:finsto:v:14:y:2010:i:3:p:397-418
    DOI: 10.1007/s00780-009-0121-0
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    References listed on IDEAS

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    1. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
    2. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    3. Pflug Georg Ch., 2006. "On distortion functionals," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-16, July.
    4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    6. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    7. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    8. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142, April.
    9. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
    10. Kasper Larsen & Traian Pirvu & Steven Shreve & Reha Tütüncü, 2005. "Satisfying convex risk limits by trading," Finance and Stochastics, Springer, vol. 9(2), pages 177-195, April.
    11. A. Cherny, 2006. "Weighted V@R and its Properties," Finance and Stochastics, Springer, vol. 10(3), pages 367-393, September.
    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. Ahmed, Shabbir & Cakmak, Ulas & Shapiro, Alexander, 2007. "Coherent risk measures in inventory problems," European Journal of Operational Research, Elsevier, vol. 182(1), pages 226-238, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. So Yeon Chun & Alexander Shapiro & Stan Uryasev, 2012. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," Operations Research, INFORMS, vol. 60(4), pages 739-756, August.
    2. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    3. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    4. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    5. Chen, Zhiping & Yang, Li, 2011. "Nonlinearly weighted convex risk measure and its application," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1777-1793, July.
    6. Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    7. Belomestny, Denis & Krätschmer, Volker, 2010. "Central limit theorems for law-invariant coherent risk measures," SFB 649 Discussion Papers 2010-052, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2014. "Quasi-Hadamard differentiability of general risk functionals and its application," Papers 1401.3167, arXiv.org, revised Feb 2015.

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    More about this item

    Keywords

    Risk functionals; Law-invariance; Asymptotic normality; M-theorems; 91B30; 62E20; 60F05; 91B28; D81; G32;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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