Characterizing a comonotonic random vector by the distribution of the sum of its components
In this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cheung, Ka Chun, 2010. "Comonotonic convex upper bound and majorization," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 154-158, October.
- Cheung, Ka Chun, 2008. "Characterization of comonotonicity using convex order," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 403-406, December.
- 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.
- Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 25, July.
- 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.
- Dhaene, Jan & Denuit, Michel & Vanduffel, Steven, 2009. "Correlation order, merging and diversification," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 325-332, December.
- Muller, Alfred, 1996. "Orderings of risks: A comparative study via stop-loss transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(3), pages 215-222, April.
- Cheung, Ka Chun, 2009. "Upper comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 35-40, August.
When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:130-136. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.