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Reducing model risk via positive and negative dependence assumptions

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  • Bignozzi, Valeria
  • Puccetti, Giovanni
  • Rüschendorf, Ludger

Abstract

We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence uncertainty spreads compared to the case where only marginals information is known. In more detail, we show that in our model the assumption of a positive dependence structure improves the best-possible lower estimate of a risk measure, while leaving unchanged its worst-possible upper risk bounds. In a similar way, we derive for convex risk measures that the assumption of a negative dependence structure leads to improved upper bounds for the risk while it does not help to increase the lower risk bounds in an essential way. As a result we find that additional assumptions on the dependence structure may result in essentially improved risk bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:17-26
    DOI: 10.1016/j.insmatheco.2014.11.004
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    References listed on IDEAS

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    Cited by:

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    2. Corrado De Vecchi & Max Nendel & Jan Streicher, 2024. "Upper Comonotonicity and Risk Aggregation under Dependence Uncertainty," Papers 2406.19242, arXiv.org.
    3. Zalzadeh, Saeed & Pellerey, Franco, 2016. "A positive dependence notion based on componentwise unimodality of copulas," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 51-57.
    4. Rüschendorf, L., 2019. "Analysis of risk bounds in partially specified additive factor models," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 115-121.
    5. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
    6. Hofert Marius & Memartoluie Amir & Saunders David & Wirjanto Tony, 2017. "Improved algorithms for computing worst Value-at-Risk," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 13-31, June.
    7. Rüschendorf Ludger & Witting Julian, 2017. "VaR bounds in models with partial dependence information on subgroups," Dependence Modeling, De Gruyter, vol. 5(1), pages 59-74, January.
    8. 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.
    9. Rüschendorf L., 2018. "Risk bounds with additional information on functionals of the risk vector," Dependence Modeling, De Gruyter, vol. 6(1), pages 102-113, June.
    10. 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.
    11. Lux, Thibaut & Papapantoleon, Antonis, 2019. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 73-83.
    12. Vytaras Brazauskas & Sahadeb Upretee, 2019. "Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions," Risks, MDPI, vol. 7(2), pages 1-16, May.
    13. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    14. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.

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