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Stochastic orders and multivariate measures of risk contagion

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  • Ortega-Jiménez, P.
  • Sordo, M.A.
  • Suárez-Llorens, A.

Abstract

Co-risk measures and risk contributions measures are used in portfolio risk analysis to assess and quantify the risk of contagion, given that one or more assets in the portfolio are in distress. In this paper, given two random vectors X and Y that represent two portfolios of n assets (n≥2) and exhibit some kind of positive dependence, we give sufficient conditions based on stochastic orders to compare the risk of contagion of the portfolios. The measures of risk contagion that we consider are the conditional value at risk (CoVaR), the conditional expected shortfall (CoES) and the recently introduced marginal mean excess (MME).

Suggested Citation

  • Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    • Handle: RePEc:eee:insuma:v:96:y:2021:i:c:p:199-207
    DOI: 10.1016/j.insmatheco.2020.11.008
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    Cited by:

    1. Tong Pu & Yifei Zhang & Yiying Zhang, 2024. "On Joint Marginal Expected Shortfall and Associated Contribution Risk Measures," Papers 2405.07549, arXiv.org.
    2. Li, Jinzhu, 2022. "Asymptotic results on marginal expected shortfalls for dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 146-168.
    3. Ortega-Jiménez, Patricia & Pellerey, Franco & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2024. "Probability equivalent level for CoVaR and VaR," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 22-35.
    4. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    5. Yiting Fan & Rui Fang, 2022. "Some Results on Measures of Interaction among Risks," Mathematics, MDPI, vol. 10(19), pages 1-19, October.
    6. Tong Pu & Yunran Wei & Yiying Zhang, 2024. "On Vulnerability Conditional Risk Measures: Comparisons and Applications in Cryptocurrency Market," Papers 2411.09676, arXiv.org.
    7. Antonia Castaño-Martínez & Gema Pigueiras & Miguel A. Sordo, 2021. "On the Increasing Convex Order of Relative Spacings of Order Statistics," Mathematics, MDPI, vol. 9(6), pages 1-12, March.
    8. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.

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    More about this item

    Keywords

    risk measure; Contagion risk; Stochastic orders; CoVaR; CoES;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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