IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v43y2008i3p403-406.html
   My bibliography  Save this article

Characterization of comonotonicity using convex order

Author

Listed:
  • Cheung, Ka Chun

Abstract

It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to the convex order. In this paper, we prove that the converse is also true, provided that each marginal distribution is continuous.

Suggested Citation

  • Cheung, Ka Chun, 2008. "Characterization of comonotonicity using convex order," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 403-406, December.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:403-406
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(08)00100-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    3. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 71-80, May.
    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. Lee, Woojoo & Ahn, Jae Youn, 2014. "On the multidimensional extension of countermonotonicity and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 68-79.
    2. Cheung, Ka Chun, 2010. "Characterizing a comonotonic random vector by the distribution of the sum of its components," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 130-136, October.
    3. Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
    4. Lee Woojoo & Ahn Jae Youn, 2017. "Measuring herd behavior: properties and pitfalls," Dependence Modeling, De Gruyter, vol. 5(1), pages 316-329, December.
    5. Chuancun Yin & Dan Zhu, 2016. "Sharp convex bounds on the aggregate sums--An alternative proof," Papers 1603.05373, arXiv.org, revised May 2016.
    6. Cheung, Ka Chun & Lo, Ambrose, 2013. "Characterizations of counter-monotonicity and upper comonotonicity by (tail) convex order," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 334-342.
    7. Mao, Tiantian & Hu, Taizhong, 2011. "A new proof of Cheung's characterization of comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 214-216, March.
    8. Changki Kim & Yangho Choi & Woojoo Lee & Jae Youn Ahn, 2013. "Analyzing Herd Behavior in Global Stock Markets: An Intercontinental Comparison," Papers 1308.3966, arXiv.org.
    9. Chuancun Yin & Dan Zhu, 2016. "Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof," Risks, MDPI, vol. 4(4), pages 1-8, September.
    10. Cheung, Ka Chun & Lo, Ambrose, 2014. "Characterizing mutual exclusivity as the strongest negative multivariate dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 180-190.

    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. Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
    2. Cheung, Ka Chun, 2009. "Applications of conditional comonotonicity to some optimization problems," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 89-93, August.
    3. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    4. Cheung, Ka Chun, 2008. "Improved convex upper bound via conditional comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 651-655, April.
    5. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524.
    6. Chuancun Yin & Dan Zhu, 2016. "Sharp convex bounds on the aggregate sums--An alternative proof," Papers 1603.05373, arXiv.org, revised May 2016.
    7. Jae Youn Ahn, 2015. "Negative Dependence Concept in Copulas and the Marginal Free Herd Behavior Index," Papers 1503.03180, arXiv.org.
    8. Chuancun Yin & Dan Zhu, 2016. "Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof," Risks, MDPI, vol. 4(4), pages 1-8, September.
    9. Cheung, Ka Chun, 2010. "Characterizing a comonotonic random vector by the distribution of the sum of its components," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 130-136, October.
    10. Cheung, Ka Chun, 2010. "Comonotonic convex upper bound and majorization," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 154-158, October.
    11. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2011. "Worst case risk measurement: Back to the future?," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 380-392.
    12. Dong, Jing & Cheung, Ka Chun & Yang, Hailiang, 2010. "Upper comonotonicity and convex upper bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 159-166, October.
    13. Vanduffel, S. & Dhaene, J. & Goovaerts, M. & Kaas, R., 2003. "The hurdle-race problem," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 405-413, October.
    14. Mao, Tiantian & Hu, Taizhong, 2011. "A new proof of Cheung's characterization of comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 214-216, March.
    15. Choo, Weihao & de Jong, Piet, 2015. "The tradeoff insurance premium as a two-sided generalisation of the distortion premium," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 238-246.
    16. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    17. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    18. Antonella Campana, 2007. "On Tail Value-at-Risk for sums of non-independent random variables with a generalized Pareto distribution," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(2), pages 169-180, December.
    19. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    20. Huang, H. & Milevsky, M. A. & Wang, J., 2004. "Ruined moments in your life: how good are the approximations?," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 421-447, June.

    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:eee:insuma:v:43:y:2008:i:3:p:403-406. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.