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Risk bounds with additional information on functionals of the risk vector

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  • Rüschendorf L.

    (Ludger Rüschendorf, University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany)

Abstract

We consider the problem of determining risk bounds for the Value at Risk for risk vectors X where besides the marginal distributions also information on the distribution or on the expectation of some functionals Tj(X), 1 ≤ j ≤ m, is available. In particular this formulation includes the case where information on subgroup sums or maxima or on the correlations or covariances is available. Based on the method of dual bounds we obtain improved risk bounds compared to the marginal case. In general the explicit calculation of the dual bounds poses a challenge. We discuss various forms of relaxation of these bounds which are accessible and in some cases even lead to sharp bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:102-113:n:6
    DOI: 10.1515/demo-2018-0006
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    References listed on IDEAS

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    1. 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.
    2. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
    3. Thibaut Lux & Antonis Papapantoleon, 2016. "Improved Fr\'echet$-$Hoeffding bounds on $d$-copulas and applications in model-free finance," Papers 1602.08894, arXiv.org, revised Jun 2017.
    4. Puccetti Giovanni & Rüschendorf Ludger, 2012. "Bounds for joint portfolios of dependent risks," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 107-132, June.
    5. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    6. 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.
    7. 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.
    8. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    9. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    10. 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.
    11. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
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    Cited by:

    1. Papapantoleon Antonis & Yanez Sarmiento Paulo, 2021. "Detection of arbitrage opportunities in multi-asset derivatives markets," Dependence Modeling, De Gruyter, vol. 9(1), pages 439-459, January.

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