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Weighted Sums of Subexponential Random Variables and Asymptotic Dependence between Returns on Reinsurance Equities

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Author Info

  • J.L. Geluk

    ()
    (Faculty of Economics, Erasmus Universiteit Rotterdam)

  • C.G. de Vries

    ()
    (Faculty of Economics, Erasmus Universiteit Rotterdam)

Abstract

Suppose are independent subexponential random variables with partial sums. We show that if the pairwise sums of the ’s 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 reinsurer’s 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 Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-102/2.

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Date of creation: 20 Sep 2004
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Handle: RePEc:dgr:uvatin:20040102

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Web page: http://www.tinbergen.nl

Related research

Keywords: Subexponentiality; regular variation; systemic risk; asymptotic dependence;

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References

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  1. 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.
  2. 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.
  3. Geluk, Jaap, 2004. "Asymptotics in the symmetrization inequality," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 63-68, August.
  4. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
  5. C.G. de vries, 2004. "The simple economics of bank fragility," WO Research Memoranda (discontinued) 755, Netherlands Central Bank, Research Department.
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Cited by:
  1. Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
  2. Jan Frederik Slijkerman, 2006. "Insurance Sector Risk," Tinbergen Institute Discussion Papers 06-062/2, Tinbergen Institute.
  3. Sheremet, Oleg & Lucas, André, 2009. "Global loss diversification in the insurance sector," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 415-425, June.
  4. Oleg Sheremet & Andr� Lucas, 2008. "Global Loss Diversification in the Insurance Sector," Tinbergen Institute Discussion Papers 08-086/2, Tinbergen Institute.
  5. 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.
  6. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.
  7. 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.

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