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Worst case risk measurement: Back to the future?

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  • Goovaerts, Marc J.
  • Kaas, Rob
  • Laeven, Roger J.A.

Abstract

This paper studies the problem of finding best-possible upper bounds on a rich class of risk measures, expressible as integrals with respect to measures, under incomplete probabilistic information. Both univariate and multivariate risk measurement problems are considered. The extremal probability distributions, generating the worst case scenarios, are also identified.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:380-392
    DOI: 10.1016/j.insmatheco.2011.06.001
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    Cited by:

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    2. Rüschendorf, L., 2019. "Analysis of risk bounds in partially specified additive factor models," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 115-121.
    3. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    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. Kunio So & Junichi Imai, 2015. "Distributional Bounds for Portfolio Risk with Tail Dependence," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 795-816, September.
    6. Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
    7. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    8. Bahl, Raj Kumari & Sabanis, Sotirios, 2021. "Model-independent price bounds for Catastrophic Mortality Bonds," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 276-291.
    9. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    10. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 10-18.
    11. Nikolay A. Andreev, 2015. "Worst-Case Approach To Strategic Optimal Portfolio Selection Under Transaction Costs And Trading Limits," HSE Working papers WP BRP 45/FE/2015, National Research University Higher School of Economics.
    12. Cornilly, D. & Rüschendorf, L. & Vanduffel, S., 2018. "Upper bounds for strictly concave distortion risk measures on moment spaces," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 141-151.
    13. 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.
    14. Asimit, Alexandru V. & Hu, Junlei & Xie, Yuantao, 2019. "Optimal robust insurance with a finite uncertainty set," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 67-81.
    15. 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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    More about this item

    Keywords

    Risk measurement; Generalized scenarios; Worst case scenario; Cones; Linear programming; Value-at-Risk; Tail-Value-at-Risk; Exponential premium;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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