IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v1y2013ip37-53n2.html
   My bibliography  Save this article

Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

Author

Listed:
  • Bernard Carole

    (Department of Statistics and Actuarial Science at the University of Waterloo)

  • Liu Yuntao

    (University of California)

  • MacGillivray Niall

    (University of Waterloo)

  • Zhang Jinyuan

    (University of British Columbia)

Abstract

Nelsen et al. [20] find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov [25] generalizes this work by giving explicit expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of [0; 1]2 are known. He shows that they are quasi-copulas and not necessarily copulas. Tankov [25] and Bernard et al. [3] both give sufficient conditions for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that both bounds are simultaneously copulas. Furthermore, we develop a novel application to quantitative risk management by computing bounds on a bivariate risk measure. This can be useful in optimal portfolio selection, in reinsurance, in pricing bivariate derivatives or in determining capital requirements when only partial information on dependence is available.

Suggested Citation

  • Bernard Carole & Liu Yuntao & MacGillivray Niall & Zhang Jinyuan, 2013. "Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence," Dependence Modeling, De Gruyter, vol. 1, pages 37-53, October.
    • Handle: RePEc:vrs:demode:v:1:y:2013:i::p:37-53:n:2
    DOI: 10.2478/demo-2013-0002
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/demo-2013-0002
    Download Restriction: no
    File URL: https://libkey.io/10.2478/demo-2013-0002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    2. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    3. Carole Bernard & Phelim P. Boyle & Steven Vanduffel, 2014. "Explicit Representation of Cost-Efficient Strategies," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 5-55.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    2. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    3. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    4. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    5. Areski Cousin & Ying Jiao & Christian y Robert & Olivier David Zerbib, 2021. "Optimal asset allocation subject to withdrawal risk and solvency constraints," Working Papers hal-03244380, HAL.
    6. Palomba, Giulio & Riccetti, Luca, 2012. "Portfolio frontiers with restrictions to tracking error volatility and value at risk," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2604-2615.
    7. Genest Christian & Scherer Matthias, 2020. "The gentleman copulist: An interview with Carlo Sempi," Dependence Modeling, De Gruyter, vol. 8(1), pages 34-44, January.
    8. Phillip Monin, 2013. "On a dynamic adaptation of the Distribution Builder approach to investment decisions," Papers 1301.0907, arXiv.org.
    9. Quesada Molina, Jose Juan & Sempi, Carlo, 2005. "Discrete quasi-copulas," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 27-41, August.
    10. Bayraktar, Erhan & Young, Virginia R., 2008. "Maximizing utility of consumption subject to a constraint on the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(4), pages 204-212, December.
    11. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2017. "My introduction to copulas: An interview with Roger Nelsen," Dependence Modeling, De Gruyter, vol. 5(1), pages 88-98, January.
    12. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    13. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    14. Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2013. "Hedging under multiple risk constraints," Papers 1309.5094, arXiv.org.
    15. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617, arXiv.org.
    16. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    17. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
    18. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    19. Carole Bernard & Steven Vanduffel & Jiang Ye, 2018. "Optimal Portfolio Under State-Dependent Expected Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.
    20. Aulbach, Stefan & Falk, Michael & Hofmann, Martin, 2012. "The multivariate Piecing-Together approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 161-170.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:demode:v:1:y:2013:i::p:37-53:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.