IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1503.03726.html
   My bibliography  Save this paper

Bounds for randomly shared risk of heavy-tailed loss factors

Author

Listed:
  • Oliver Kley
  • Claudia Kluppelberg

Abstract

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the components of $V$ and arbitrary dependence structure in a multivariate regular variation setting. Upper and lower bounds are given by asymptotically independent and fully dependent components of $V$ with respect to the tail index $\alpha$ being smaller or larger than 1. Counterexamples, where for non-linear aggregation functions no bounds are available, complete the picture.

Suggested Citation

  • Oliver Kley & Claudia Kluppelberg, 2015. "Bounds for randomly shared risk of heavy-tailed loss factors," Papers 1503.03726, arXiv.org, revised Apr 2016.
    • Handle: RePEc:arx:papers:1503.03726
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1503.03726
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Caccioli, Fabio & Shrestha, Munik & Moore, Cristopher & Farmer, J. Doyne, 2014. "Stability analysis of financial contagion due to overlapping portfolios," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 233-245.
    2. Chen Chen & Garud Iyengar & Ciamac C. Moallemi, 2013. "An Axiomatic Approach to Systemic Risk," Management Science, INFORMS, vol. 59(6), pages 1373-1388, June.
    3. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    4. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    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. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2015. "Conditional risk measures in a bipartite market structure," Papers 1510.00616, arXiv.org.
    2. Kley, Oliver & Klüppelberg, Claudia & Paterlini, Sandra, 2020. "Modelling extremal dependence for operational risk by a bipartite graph," Journal of Banking & Finance, Elsevier, vol. 117(C).
    3. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.

    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. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.
    2. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    3. Paul Glasserman & H. Peyton Young, 2016. "Contagion in Financial Networks," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 779-831, September.
    4. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2015. "Conditional risk measures in a bipartite market structure," Papers 1510.00616, arXiv.org.
    5. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    6. Glasserman, Paul & Young, H. Peyton, 2016. "Contagion in financial networks," LSE Research Online Documents on Economics 68681, London School of Economics and Political Science, LSE Library.
    7. Kerstin Awiszus & Agostino Capponi & Stefan Weber, 2020. "Market Efficient Portfolios in a Systemic Economy," Papers 2003.10121, arXiv.org, revised May 2021.
    8. Nils Detering & Thilo Meyer-Brandis & Konstantinos Panagiotou & Daniel Ritter, 2020. "Suffocating Fire Sales," Papers 2006.08110, arXiv.org, revised Nov 2021.
    9. Francesca Biagini & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2020. "On fairness of systemic risk measures," Finance and Stochastics, Springer, vol. 24(2), pages 513-564, April.
    10. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "Measuring risk contagion in financial networks with CoVaR," Papers 2309.15511, arXiv.org, revised May 2025.
    11. Paul Glasserman & H. Peyton Young, 2015. "Contagion in Financial Networks," Working Papers 15-21, Office of Financial Research, US Department of the Treasury.
    12. Yongli Li & Guanghe Liu & Paolo Pin, 2018. "Network-based risk measurements for interbank systems," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-18, July.
    13. Raffestin, Louis, 2014. "Diversification and systemic risk," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 85-106.
    14. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    15. Bichuch, Maxim & Feinstein, Zachary, 2022. "A repo model of fire sales with VWAP and LOB pricing mechanisms," European Journal of Operational Research, Elsevier, vol. 296(1), pages 353-367.
    16. Ding, Jing & Jiang, Lei & Liu, Xiaohui & Peng, Liang, 2023. "Nonparametric tests for market timing ability using daily mutual fund returns," Journal of Economic Dynamics and Control, Elsevier, vol. 150(C).
    17. 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.
    18. Guo Weilong & Minca Andreea & Wang Li, 2016. "The topology of overlapping portfolio networks," Statistics & Risk Modeling, De Gruyter, vol. 33(3-4), pages 139-155, December.
    19. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.
    20. Fricke, Daniel & Roukny, Tarik, 2020. "Generalists and specialists in the credit market," Journal of Banking & Finance, Elsevier, vol. 112(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1503.03726. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.