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Range Value-at-Risk bounds for unimodal distributions under partial information

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  • Bernard, Carole
  • Kazzi, Rodrigue
  • Vanduffel, Steven

Abstract

In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean, variance, and feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one, which in a second step can be solved using standard methods. The novel approach we propose makes it possible to obtain analytical results for all probability levels and is moreover amendable to other situations of interest. Specifically, we apply our method to obtain risk bounds in the case of a portfolio loss that is non-negative (as is often the case in practice) and whose variance is possibly infinite. Numerical illustrations show that in various cases of interest we obtain bounds that are of practical importance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:94:y:2020:i:c:p:9-24
    DOI: 10.1016/j.insmatheco.2020.05.013
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    References listed on IDEAS

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    1. Carole Bernard & Michel Denuit & Steven Vanduffel, 2018. "Measuring Portfolio Risk Under Partial Dependence Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(3), pages 843-863, September.
    2. Bignozzi, Valeria & Puccetti, Giovanni & Rüschendorf, Ludger, 2015. "Reducing model risk via positive and negative dependence assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 17-26.
    3. 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.
    4. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    5. Puccetti Giovanni & Rüschendorf Ludger, 2012. "Bounds for joint portfolios of dependent risks," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 107-132, June.
    6. Carole Bernard & Don McLeish, 2016. "Algorithms for Finding Copulas Minimizing Convex Functions of Sums," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-26, October.
    7. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    8. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    9. 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.
    10. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    11. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    12. Kris Boudt & Edgars Jakobsons & Steven Vanduffel, 2018. "Block rearranging elements within matrix columns to minimize the variability of the row sums," 4OR, Springer, vol. 16(1), pages 31-50, March.
    13. 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.
    14. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    15. Vandendorpe, Antoine & Ho, Ngoc-Diep & Vanduffel, Steven & Van Dooren, Paul, 2008. "On the parameterization of the CreditRisk + model for estimating credit portfolio risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 736-745, April.
    16. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    17. Puccetti Giovanni & Rüschendorf Ludger & Manko Dennis, 2016. "VaR bounds for joint portfolios with dependence constraints," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-14, December.
    18. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
    19. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    20. Kaas, R. & Goovaerts, M. J., 1986. "Best bounds for positive distributions with fixed moments," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 87-92, January.
    21. 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.
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    4. Wang, Jujie & Cui, Quan & He, Maolin, 2022. "Hybrid intelligent framework for carbon price prediction using improved variational mode decomposition and optimal extreme learning machine," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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