IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20040102.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/04102.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    2. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
    3. 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.
    4. Rockinger, Michael & Poon, Ser-Huang & Tawn, Jonathan, 2001. "New Extreme-Value Dependence Measures and Finance Applications," CEPR Discussion Papers 2762, C.E.P.R. Discussion Papers.
    5. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    6. 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.
    7. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    8. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    9. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    10. De Vries, C.G., 2005. "The simple economics of bank fragility," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 803-825, April.
    11. Geluk, Jaap, 2004. "Asymptotics in the symmetrization inequality," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 63-68, August.
    12. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
    13. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.
    3. 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.
    4. Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. De Vries, C.G., 2005. "The simple economics of bank fragility," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 803-825, April.
    2. K. Minderhoud, 2006. "Systemic Risk in the Dutch Financial Sector," De Economist, Springer, vol. 154(2), pages 177-195, June.
    3. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    4. Straetmans, Stefan & Chaudhry, Sajid M., 2015. "Tail risk and systemic risk of US and Eurozone financial institutions in the wake of the global financial crisis," Journal of International Money and Finance, Elsevier, vol. 58(C), pages 191-223.
    5. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    6. Cumperayot, Phornchanok & Kouwenberg, Roy, 2013. "Early warning systems for currency crises: A multivariate extreme value approach," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 151-171.
    7. Hartmann, Philipp & Straetmans, Stefan & de Vries, Casper, 2004. "Fundamentals and joint currency crises," Working Paper Series 324, European Central Bank.
    8. Candelon, Bertrand & Straetmans, Stefan, 2006. "Testing for multiple regimes in the tail behavior of emerging currency returns," Journal of International Money and Finance, Elsevier, vol. 25(7), pages 1187-1205, November.
    9. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    10. S. T. M. Straetmans & W. F. C. Verschoor & C. C. P. Wolff, 2008. "Extreme US stock market fluctuations in the wake of 9|11," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 17-42.
    11. Straetmans, Stefan & Candelon, Bertrand, 2013. "Long-term asset tail risks in developed and emerging markets," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 1832-1844.
    12. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.
    13. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    14. Pais, Amelia & Stork, Philip A., 2011. "Contagion risk in the Australian banking and property sectors," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 681-697, March.
    15. Balla, Eliana & Ergen, Ibrahim & Migueis, Marco, 2014. "Tail dependence and indicators of systemic risk for large US depositories," Journal of Financial Stability, Elsevier, vol. 15(C), pages 195-209.
    16. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    17. Chollete, Loran & Ismailescu, Iuliana & Lu, Ching-Chih, 2014. "Dependence between Extreme Events in the Real and Financial Sectors," UiS Working Papers in Economics and Finance 2014/12, University of Stavanger.
    18. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    19. Zhou, Chen, 2013. "The impact of imposing capital requirements on systemic risk," Journal of Financial Stability, Elsevier, vol. 9(3), pages 320-329.
    20. Longin, Francois, 2005. "The choice of the distribution of asset returns: How extreme value theory can help?," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 1017-1035, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20040102. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.