Some proposals about multivariate risk measurement
In actuarial literature the properties of risk measures or insurance premium principles have been extensively studied. In our work we propose a characterization of some particular classes of multivariate and bivariate risk measures. Given two random variables we can define an univariate integral stochastic ordering by considering a set of functions that, through their peculiar properties, originate different stochastic orderings. These stochastic order relations of integral form may be extended to cover also the case of random vectors. It is, in fact, proposed a kind of stop-loss premium, and then a stop-loss order in the multivariate setting and some equivalent conditions. We propose an axiomatic approach based on a minimal set of properties which characterizes an insurance premium principle. In the univariate case we know that Conditional Value at Risk can be represented through distortion risk measures and a distortion risk measure can be viewed as a combination of CVaRs, we propose a generalization of this result in a multivariate framework. In the bivariate case we want to compare the concept of risk measure to that one of concordance measure when the marginals are given.
|Date of creation:||May 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: ++39 041 2346910-6911
Fax: ++ 39 041 5221756
Web page: http://www.dma.unive.it/
More information through EDIRC
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.:
- Marta Cardin & Graziella Pacelli, 2006. "On the characterization of convex premium principles," Working Papers 142, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Scarsini, Marco, 1985. "Stochastic dominance with pair-wise risk aversion," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 187-201, April.
- Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
- Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
- Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
- Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
- Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
When requesting a correction, please mention this item's handle: RePEc:vnm:wpaper:165. 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: (Marco LiCalzi)
If references are entirely missing, you can add them using this form.