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Risk in a Large Claims Insurance Market with Bipartite Graph Structure

Author

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  • Oliver Kley

    (Center for Mathematical Sciences, Technical University of Munich, 85748 Garching, Boltzmannstrasse 3, Germany)

  • Claudia Klüppelberg

    (Center for Mathematical Sciences, Technical University of Munich, 85748 Garching, Boltzmannstrasse 3, Germany)

  • Gesine Reinert

    (Department of Statistics, University of Oxford, Oxford OX1 3TG, United Kingdom)

Abstract

We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the value-at-risk and the conditional tail expectation. We show that the dependence on the network structure plays a fundamental role in their asymptotic behaviour. As is well known in a nonnetwork setting, if the Pareto exponent is larger than 1, then for the individual agent (reinsurance company) diversification is beneficial, whereas when it is less than 1, concentration on a few objects is the better strategy.An additional aspect of this paper is the amount of uninsured losses that are covered by society. In our setting of networks of agents, diversification is never detrimental to the amount of uninsured losses. If the Pareto-tailed claims have finite mean, diversification is never detrimental, to society or individual agents. By contrast, if the Pareto-tailed claims have infinite mean, a conflicting situation may arise between the incentives of individual agents and the interest of some regulator to keep the risk for society small. We explain the influence of the network structure on diversification effects in different network scenarios.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:5:p:1159-1176
    DOI: 10.1287/opre.2016.1502
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Daniel Ritter, 2019. "Mathematical Modeling of Systemic Risk in Financial Networks: Managing Default Contagion and Fire Sales," Papers 1911.07313, arXiv.org.
    2. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Insurance risk analysis of financial networks vulnerable to a shock," European Journal of Operational Research, Elsevier, vol. 301(2), pages 756-771.
    3. Rama Cont & Darrell Duffie & Paul Glasserman & Chris Rogers & Fernando Vega-Redondo, 2016. "Preface to the Special Issue on Systemic Risk: Models and Mechanisms," Operations Research, INFORMS, vol. 64(5), pages 1053-1055, October.
    4. Das Bikramjit & Fasen-Hartmann Vicky, 2019. "Conditional excess risk measures and multivariate regular variation," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 1-23, December.
    5. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Discussion Paper 2023-001, Tilburg University, Center for Economic Research.
    6. Amini, Hamed & Minca, Andreea & Sulem, Agnès, 2017. "Optimal equity infusions in interbank networks," Journal of Financial Stability, Elsevier, vol. 31(C), pages 1-17.
    7. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "Measuring risk contagion in financial networks with CoVaR," Papers 2309.15511, arXiv.org, revised Jun 2024.
    8. Nils Detering & Thilo Meyer-Brandis & Konstantinos Panagiotou & Daniel Ritter, 2020. "Suffocating Fire Sales," Papers 2006.08110, arXiv.org, revised Nov 2021.
    9. Ariah Klages-Mundt & Andreea Minca, 2020. "Cascading Losses in Reinsurance Networks," Management Science, INFORMS, vol. 66(9), pages 4246-4268, September.
    10. 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).
    11. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    12. Einmahl, John & Krajina, Andrea, 2023. "Empirical Likelihood Based Testing for Multivariate Regular Variation," Other publications TiSEM 261583f5-c571-48c6-8cea-9, Tilburg University, School of Economics and Management.
    13. Ariah Klages-Mundt & Andreea Minca, 2018. "Cascading Losses in Reinsurance Networks," Papers 1805.12222, arXiv.org, revised Mar 2020.
    14. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    15. Bikramjit Das & Vicky Fasen-Hartmann & Claudia Kluppelberg, 2019. "Tail probabilities of random linear functions of regularly varying random vectors," Papers 1904.06824, arXiv.org, revised Jun 2020.

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