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Risk measures, distortion parameters, and their empirical estimation

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  • Jones, Bruce L.
  • Zitikis, Ricardas

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  • 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.
    • Handle: RePEc:eee:insuma:v:41:y:2007:i:2:p:279-297
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    References listed on IDEAS

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    1. Landsman, Zinoviy & Sherris, Michael, 2001. "Risk measures and insurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 103-115, August.
    2. 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.
    3. Lynn Wirch, Julia & Hardy, Mary R., 1999. "A synthesis of risk measures for capital adequacy," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 337-347, December.
    4. 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.
    5. Jan Dhaene & Mark Goovaerts & Rob Kaas, 2003. "Economic Capital Allocation Derived from Risk Measures," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(2), pages 44-56.
    6. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    7. 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.
    8. Bruce L. Jones & Ricardas Zitikis, 2005. "Testing for the order of risk measures: an application of L-statistics in actuarial science," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 193-211.
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    Cited by:

    1. 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.
    2. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2012. "Comparison of risks based on the expected proportional shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 292-302.
    3. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    4. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
    5. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    6. Brahimi, Brahim & Abdelli, Jihane, 2016. "Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 135-143.
    7. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    8. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
    9. Wozabal, Nancy, 2009. "Uniform limit theorems for functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1450-1455, June.
    10. Haruyoshi Ito & Jing Ai & Akihiko Ozawa, 2016. "Managing Weather Risks: The Case of J. League Soccer Teams in Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 877-912, December.
    11. Henryk Zähle, 2011. "Rates of almost sure convergence of plug-in estimates for distortion risk measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 267-285, September.
    12. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
    13. 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.
    14. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
    15. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    16. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    17. Georg Pflug & Nancy Wozabal, 2010. "Asymptotic distribution of law-invariant risk functionals," Finance and Stochastics, Springer, vol. 14(3), pages 397-418, September.
    18. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    19. Asimit, Alexandru V. & Li, Jinzhu, 2016. "Extremes for coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 332-341.
    20. Sendov, Hristo S. & Wang, Ying & Zitikis, Ricardas, 2011. "Log-supermodularity of weight functions, ordering weighted losses, and the loading monotonicity of weighted premiums," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 257-264, March.
    21. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.
    22. Labopin-Richard T. & Gamboa F. & Garivier A. & Iooss B., 2016. "Bregman superquantiles. Estimation methods and applications," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, March.
    23. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    24. Kamal Boukhetala & Jean-François Dupuy, 2014. "Colloque International Book of Abstracts Edité par K. Boukhetala et J.F Dupuy," Post-Print hal-01086342, HAL.

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