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Bounds for Functions of Dependent Risks


  • Paul Embrechts


  • Giovanni Puccetti



No abstract is available for this item.

Suggested Citation

  • Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
  • Handle: RePEc:spr:finsto:v:10:y:2006:i:3:p:341-352
    DOI: 10.1007/s00780-006-0005-5

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    References listed on IDEAS

    1. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
    2. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
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    Cited by:

    1. Stefan Mittnik & Sandra Paterlini & Tina Yener, 2011. "Operational–risk Dependencies and the Determination of Risk Capital," Center for Economic Research (RECent) 070, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    2. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    3. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    4. McNeil, Alexander J. & Smith, Andrew D., 2012. "Multivariate stress scenarios and solvency," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 299-308.
    5. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
    6. Thibaut Lux & Antonis Papapantoleon, 2016. "Model-free bounds on Value-at-Risk using partial dependence information," Papers 1610.09734,, revised Jun 2017.
    7. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    8. Embrechts, Paul & Puccetti, Giovanni, 2010. "Bounds for the sum of dependent risks having overlapping marginals," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 177-190, January.
    9. repec:bpj:strimo:v:34:y:2017:i:1-2:p:13-31:n:3 is not listed on IDEAS
    10. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2011. "Worst case risk measurement: Back to the future?," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 380-392.
    11. Laeven, Roger J.A., 2009. "Worst VaR scenarios: A remark," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 159-163, April.
    12. Raphael Hauser & Sergey Shahverdyan & Paul Embrechts, 2014. "A General Duality Relation with Applications in Quantitative Risk Management," Papers 1410.0852,
    13. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
    14. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias, 2015. "A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-14, October.
    15. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057,, revised Jan 2016.
    16. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    17. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    18. Goncalves Marcelo & Fabris Antonio & Kolev Nikolai, 2008. "Bounds for Distorted Risk Measures," Stochastics and Quality Control, De Gruyter, vol. 23(2), pages 243-255, January.
    19. Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2015. "Actuarial Applications and Estimation of Extended~CreditRisk$^+$," Papers 1505.04757,, revised Apr 2017.
    20. Ludger Rüschendorf, 2012. "Worst case portfolio vectors and diversification effects," Finance and Stochastics, Springer, vol. 16(1), pages 155-175, January.
    21. Goncalves Marcelo & Kolev Nikolai & Fabris Antonio Elias, 2008. "Bounds for Quantile-Based Risk Measures of Functions of Dependent Random Variables," Stochastics and Quality Control, De Gruyter, vol. 23(1), pages 55-70, January.
    22. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    23. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    24. Cascos, Ignacio & Molchanov, Ilya, 2013. "Choosing a random distribution with prescribed risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 599-605.

    More about this item


    Copulas; Dependent risks; Dependence bounds; Fréchet bounds; 60E15; 60E05; G10;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)


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