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Bounds for randomly shared risk of heavy-tailed loss factors

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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