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Optimal risk allocation in reinsurance networks

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  • Bäuerle, Nicole
  • Glauner, Alexander

Abstract

In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties. In our setting we assume that there are n insurance companies, each bearing a certain risk, and one representative reinsurer. The optimization problem is to minimize the sum of all capital requirements of the insurers where we assume that all insurance companies use a form of Range-Value-at-Risk. We show that in case all insurers use Value-at-Risk and the reinsurer’s premium principle satisfies monotonicity, then layer reinsurance treaties are socially optimal. For this result we do not need any dependence structure between the risks. In the general setting with Range-Value-at-Risk we obtain again the optimality of layer reinsurance treaties under further assumptions, in particular under the assumption that the individual risks are positively dependent through the stochastic ordering. Our results include the findings in Chi and Tan (2013) in the special case n=1. At the end, we discuss the difference between socially optimal reinsurance treaties and individually optimal ones by looking at a number of special cases.

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  • Bäuerle, Nicole & Glauner, Alexander, 2018. "Optimal risk allocation in reinsurance networks," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 37-47.
    • Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:37-47
    DOI: 10.1016/j.insmatheco.2018.06.009
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    Cited by:

    1. Nicole Bäuerle & Alexander Glauner, 2021. "Minimizing spectral risk measures applied to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 35-69, August.
    2. Ernest Aboagye & Vali Asimit & Tsz Chai Fung & Liang Peng & Qiuqi Wang, 2024. "A Revisit of the Optimal Excess-of-Loss Contract," Papers 2405.00188, arXiv.org.
    3. Bäuerle, Nicole & Glauner, Alexander, 2022. "Markov decision processes with recursive risk measures," European Journal of Operational Research, Elsevier, vol. 296(3), pages 953-966.
    4. Nicole Bauerle & Tomer Shushi, 2019. "Risk Management with Tail Quasi-Linear Means," Papers 1902.06941, arXiv.org, revised Jan 2020.
    5. Alexander Glauner, 2020. "Dynamic Reinsurance in Discrete Time Minimizing the Insurer's Cost of Capital," Papers 2012.09648, arXiv.org.
    6. Kotlicki, Artur & Austin, Andrea & Humphry, David & Burnett, Hanna & Ridgill, Philip & Smith, Sam, 2023. "Network analysis of the UK reinsurance market," Bank of England working papers 1000, Bank of England.
    7. Nicole Bauerle & Alexander Glauner, 2020. "Minimizing Spectral Risk Measures Applied to Markov Decision Processes," Papers 2012.04521, arXiv.org.
    8. Nicole Bauerle & Alexander Glauner, 2020. "Markov Decision Processes with Recursive Risk Measures," Papers 2010.07220, arXiv.org.

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