Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities
AbstractSuppose are independent subexponential random variables with partial sums. We show that if the pairwise sums of the âs are subexponential, then is subexponential and . The result is applied to give conditions under which as , where are constants such that is a.s. convergent. Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry expose different reinsurers to the same subexponential risks on both sides of their balance sheets. This implies that reinsurerâs equity returns can be asymptotically dependent, exposing the industry to systemic risk. Published in Insurance, Mathematics and Economics . (2006, 38, 39-56.)
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 38 (2006)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/inca/505554
Other versions of this item:
- J.L. Geluk & C.G. de Vries, 2004. "Weighted Sums of Subexponential Random Variables and Asymptotic Dependence between Returns on Reinsurance Equities," Tinbergen Institute Discussion Papers 04-102/2, Tinbergen Institute.
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.:
- Jansen, Dennis W & de Vries, Casper G, 1991.
"On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective,"
The Review of Economics and Statistics,
MIT Press, vol. 73(1), pages 18-24, February.
- Dennis Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- C.G. de vries, 2004.
"The simple economics of bank fragility,"
WO Research Memoranda (discontinued)
755, Netherlands Central Bank, Research Department.
- Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
- Davis, Richard & Resnick, Sidney, 1988. "Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 41-68, November.
- Geluk, Jaap, 2004. "Asymptotics in the symmetrization inequality," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 63-68, August.
- repec:dgr:uvatin:2008086 is not listed on IDEAS
- Sheremet, Oleg & Lucas, André, 2009.
"Global loss diversification in the insurance sector,"
Insurance: Mathematics and Economics,
Elsevier, vol. 44(3), pages 415-425, June.
- Oleg Sheremet & Andr� Lucas, 2008. "Global Loss Diversification in the Insurance Sector," Tinbergen Institute Discussion Papers 08-086/2, Tinbergen Institute.
- Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
- Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
- repec:dgr:uvatin:2007023 is not listed on IDEAS
- Jan Frederik Slijkerman, 2006. "Insurance Sector Risk," Tinbergen Institute Discussion Papers 06-062/2, Tinbergen Institute.
- Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
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