Stochastic comparisons of distorted variability measures
In this paper, we consider the dispersive order and the excess wealth order to compare the variability of distorted distributions. We know from Sordo (2009a) that the excess wealth order can be characterized in terms of a class of variability measures associated to the tail conditional distribution which includes, as a particular measure, the tail variance. Given that the tail conditional distribution is a particular distorted distribution, a natural question is whether this result can be extended to include other classes of variability measures associated to general distorted distributions. As we show in this paper, the answer is yes, by focusing on distorted distributions associated to concave distortion functions. For distorted distributions associated to more general distortions, the characterizations are stated in terms of the stronger dispersive order.
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.:
- Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
- Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
- Denneberg, Dieter, 1990. "Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 20(02), pages 181-190, November.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Sordo, Miguel A., 2009. "On the relationship of location-independent riskier order to the usual stochastic order," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 155-157, January.
- Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
- Hu, Taizhong & Chen, Jing & Yao, Junchao, 2006. "Preservation of the location independent risk order under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 406-412, April.
- Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(01), pages 71-92, May.
- Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004.
"Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
- Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
- Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
- Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
- Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(02), pages 433-462, November.
- Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:11-17. 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: (Zhang, Lei)
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.