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Cascading Losses in Reinsurance Networks

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  • Ariah Klages-Mundt
  • Andreea Minca

Abstract

We develop a model for contagion in reinsurance networks by which primary insurers' losses are spread through the network. Our model handles general reinsurance contracts, such as typical excess of loss contracts. We show that simpler models existing in the literature--namely proportional reinsurance--greatly underestimate contagion risk. We characterize the fixed points of our model and develop efficient algorithms to compute contagion with guarantees on convergence and speed under conditions on network structure. We characterize exotic cases of problematic graph structure and nonlinearities, which cause network effects to dominate the overall payments in the system. We lastly apply our model to data on real world reinsurance networks. Our simulations demonstrate the following: (1) Reinsurance networks face extreme sensitivity to parameters. A firm can be wildly uncertain about its losses even under small network uncertainty. (2) Our sensitivity results reveal a new incentive for firms to cooperate to prevent fraud, as even small cases of fraud can have outsized effect on the losses across the network. (3) Nonlinearities from excess of loss contracts obfuscate risks and can cause excess costs in a real world system.

Suggested Citation

  • Ariah Klages-Mundt & Andreea Minca, 2018. "Cascading Losses in Reinsurance Networks," Papers 1805.12222, arXiv.org, revised Mar 2020.
  • Handle: RePEc:arx:papers:1805.12222
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    File URL: http://arxiv.org/pdf/1805.12222
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    References listed on IDEAS

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    Cited by:

    1. Barnett, William A. & Wang, Xue & Xu, Hai-Chuan & Zhou, Wei-Xing, 2022. "Hierarchical contagions in the interdependent financial network," Journal of Financial Stability, Elsevier, vol. 61(C).
    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. Tim J. Boonen & Yuyu Chen & Xia Han & Qiuqi Wang, 2024. "Optimal insurance design with Lambda-Value-at-Risk," Papers 2408.09799, arXiv.org.
    4. Zachary Feinstein & Andreas Sojmark, 2022. "Endogenous distress contagion in a dynamic interbank model: how possible future losses may spell doom today," Papers 2211.15431, arXiv.org, revised Aug 2024.
    5. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Jump Risk," Papers 2108.00799, arXiv.org, revised Feb 2023.
    6. Zachary Feinstein & T. R. Hurd, 2020. "Contingent Convertible Obligations and Financial Stability," Papers 2006.01037, arXiv.org, revised Oct 2022.
    7. Tathagata Banerjee & Zachary Feinstein, 2018. "Pricing of debt and equity in a financial network with comonotonic endowments," Papers 1810.01372, arXiv.org, revised Sep 2021.
    8. Liu, Haiyan & Mao, Tiantian, 2022. "Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 393-417.
    9. Lei Li & Kun Qin & Desheng Wu, 2023. "A Hybrid Approach for the Assessment of Risk Spillover to ESG Investment in Financial Networks," Sustainability, MDPI, vol. 15(7), pages 1-16, April.

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