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Worst VaR scenarios with given marginals and measures of association

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  • Kaas, Rob
  • Laeven, Roger J.A.
  • Nelsen, Roger B.

Abstract

This paper studies the problem of finding best-possible upper bounds on the Value-at-Risk for a function of two random variables when the marginal distributions are known and additional nonparametric information on the dependence structure, such as the value of a measure of association, is available. The same problem for the Tail-Value-at-Risk is also briefly discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:146-158
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    References listed on IDEAS

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    15. Yiting Fan & Rui Fang, 2022. "Some Results on Measures of Interaction among Risks," Mathematics, MDPI, vol. 10(19), pages 1-19, October.
    16. Sordo, M.A. & Bello, A.J. & Suárez-Llorens, A., 2018. "Stochastic orders and co-risk measures under positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 105-113.
    17. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    18. Zhi Chen & Weijun Xie, 2021. "Sharing the value‐at‐risk under distributional ambiguity," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 531-559, January.
    19. 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.
    20. Ye, Wuyi & Zhou, Yi & Chen, Pengzhan & Wu, Bin, 2024. "A simulation-based method for estimating systemic risk measures," European Journal of Operational Research, Elsevier, vol. 313(1), pages 312-324.
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    22. Cascos, Ignacio & Molchanov, Ilya, 2013. "Choosing a random distribution with prescribed risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 599-605.

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