Stochastic comparisons for allocations of policy limits and deductibles with applications
AbstractIn this paper, we study the problem of comparing losses of a policyholder who has an increasing utility function when the form of coverage is policy limit and deductible. The total retained losses of a policyholder are ordered in the usual stochastic order sense when Xi(i=1,...,n) are ordered with respect to the likelihood ratio order. The parallel results for the case of deductibles are obtained in the same way. It is shown that the ordering of the losses are related to the characteristics (log-concavity or log-convexity) of distributions of the risks. As an application of the comparison results, the optimal problems of allocations of policy limits and deductibles are studied in usual stochastic order sense and the closed-form optimal solutions are obtained in some special cases.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 48 (2011)
Issue (Month): 3 (May)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
Usual stochastic order Likelihood ratio order Majorization order Policy limit Policy deductible Optimal solution;
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.:
- Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1717-1723, August.
- Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
- Bagnoli, M. & Bergstrom, T., 1989.
"Log-Concave Probability And Its Applications,"
89-23, Michigan - Center for Research on Economic & Social Theory.
- Zhuang, Weiwei & Chen, Zijin & Hu, Taizhong, 2009. "Optimal allocation of policy limits and deductibles under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 409-414, June.
- Hua, Lei & Cheung, Ka Chun, 2008. "Worst allocations of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 93-98, August.
- Mi, J. & Shi, W. & Zhou, Y.Y., 2008. "Some properties of convolutions of Pascal and Erlang random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2378-2387, October.
- Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
- Arnold, Barry C. & Villaseñor, Jose A., 1986. "Lorenz ordering of means and medians," Statistics & Probability Letters, Elsevier, vol. 4(1), pages 47-49, January.
- Korwar, Ramesh M., 2002. "On Stochastic Orders for Sums of Independent Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 344-357, February.
- Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
- Li, Xiaohu & You, Yinping, 2012. "On allocation of upper limits and deductibles with dependent frequencies and comonotonic severities," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 423-429.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
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.