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Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities

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  • Geluk, J.L.
  • De Vries, C.G.

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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  • Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
  • Handle: RePEc:eee:insuma:v:38:y:2006:i:1:p:39-56
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    Cited by:

    1. 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.
    2. Sheremet, Oleg & Lucas, André, 2009. "Global loss diversification in the insurance sector," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 415-425, June.
    3. Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
    4. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, 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.

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