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

Author

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  • 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.)

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20040102
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    References listed on IDEAS

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    Cited by:

    1. Sheremet, Oleg & Lucas, André, 2009. "Global loss diversification in the insurance sector," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 415-425, June.
    2. 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.
    3. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
    4. 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.
    5. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.
    6. 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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