IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.19902.html
   My bibliography  Save this paper

Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information

Author

Listed:
  • Mengshuo Zhao
  • Chuancun Yin

Abstract

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the corresponding distortion functions. As examples, extremal cases of VaR, TVaR and RVaR are derived.

Suggested Citation

  • Mengshuo Zhao & Chuancun Yin, 2024. "Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information," Papers 2409.19902, arXiv.org.
    • Handle: RePEc:arx:papers:2409.19902
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.19902
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    2. 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.
    3. Cai, Jun & Liu, Fangda & Yin, Mingren, 2024. "Worst-case risk measures of stop-loss and limited loss random variables under distribution uncertainty with applications to robust reinsurance," European Journal of Operational Research, Elsevier, vol. 318(1), pages 310-326.
    4. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    5. Shao, Hui & Zhang, Zhe George, 2023. "Distortion risk measure under parametric ambiguity," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1159-1172.
    6. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    7. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    8. Wang, Qiuqi & Wang, Ruodu & Wei, Yunran, 2020. "Distortion Riskmetrics On General Spaces," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 827-851, September.
    9. 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.
    10. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    11. Liu, Fangda & Cai, Jun & Lemieux, Christiane & Wang, Ruodu, 2020. "Convex risk functionals: Representation and applications," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 66-79.
    12. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mengshuo Zhao & Narayanaswamy Balakrishnan & Chuancun Yin, 2024. "Extremal cases of distortion risk measures with partial information," Papers 2404.13637, arXiv.org, revised Oct 2024.
    2. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.
    3. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.
    4. Shao, Hui & Zhang, Zhe George, 2023. "Distortion risk measure under parametric ambiguity," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1159-1172.
    5. Fabio Bellini & Tolulope Fadina & Ruodu Wang & Yunran Wei, 2020. "Parametric measures of variability induced by risk measures," Papers 2012.05219, arXiv.org, revised Apr 2022.
    6. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    7. Barrieu, Pauline & Scandolo, Giacomo, 2014. "Assessing financial model risk," LSE Research Online Documents on Economics 60084, London School of Economics and Political Science, LSE Library.
    8. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.
    9. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    10. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    11. Onur Babat & Juan C. Vera & Luis F. Zuluaga, 2021. "Computing near-optimal Value-at-Risk portfolios using Integer Programming techniques," Papers 2107.07339, arXiv.org.
    12. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    13. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    14. Ruodu Wang & Yunran Wei, 2020. "Risk functionals with convex level sets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1337-1367, October.
    15. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    16. Weiping Wu & Yu Lin & Jianjun Gao & Ke Zhou, 2023. "Mean-variance hybrid portfolio optimization with quantile-based risk measure," Papers 2303.15830, arXiv.org, revised Apr 2023.
    17. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
    18. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    19. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    20. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2409.19902. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.