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Comparison of conditional distributions in portfolios of dependent risks

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  • Sordo, Miguel A.
  • Suárez-Llorens, Alfonso
  • Bello, Alfonso J.

Abstract

Given a portfolio of risks, we study the marginal behavior of the ith risk under an adverse event, such as an unusually large loss in the portfolio or, in the case of a portfolio with a positive dependence structure, to an unusually large loss for another risk. By considering some particular conditional risk distributions, we formalize, in several ways, the intuition that the ith component of the portfolio is riskier when it is part of a positive dependent random vector than when it is considered alone. We also study, given two random vectors with a fixed dependence structure, the circumstances under which the existence of some stochastic orderings among their marginals implies an ordering among the corresponding conditional risk distributions.

Suggested Citation

  • Sordo, Miguel A. & Suárez-Llorens, Alfonso & Bello, Alfonso J., 2015. "Comparison of conditional distributions in portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 62-69.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:62-69
    DOI: 10.1016/j.insmatheco.2014.11.008
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    References listed on IDEAS

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    14. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
    15. Cai, Jun & Wei, Wei, 2012. "On the invariant properties of notions of positive dependence and copulas under increasing transformations," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 43-49.
    16. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
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    Cited by:

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    2. Alfonso J. Bello & Julio Mulero & Miguel A. Sordo & Alfonso Suárez-Llorens, 2020. "On Partial Stochastic Comparisons Based on Tail Values at Risk," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    3. P. G. Sankaran & M. Dileep Kumar, 2019. "Reliability properties of proportional hazards relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 441-456, May.
    4. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    5. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    6. 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.
    7. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2017. "Multiple risk measures for multivariate dynamic heavy–tailed models," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 1-32.
    8. Bernardi Mauro & Roy Cerqueti & Arsen Palestini, 2016. "Allocation of risk capital in a cost cooperative game induced by a modified Expected Shortfall," Papers 1608.02365, arXiv.org.
    9. Hélène Cossette & Mélina Mailhot & Étienne Marceau & Mhamed Mesfioui, 2016. "Vector-Valued Tail Value-at-Risk and Capital Allocation," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 653-674, September.
    10. Arriaza, Antonio & Navarro, Jorge & Ortega-Jiménez, Patricia, 2024. "Risk times in mission-oriented systems," LIDAM Discussion Papers ISBA 2024017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    12. 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.
    13. Sordo, Miguel A., 2016. "A multivariate extension of the increasing convex order to compare risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 224-230.
    14. 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.
    15. 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.

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