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Optimal reinsurance for risk over surplus ratios

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  • Erik B{o}lviken
  • Yinzhi Wang

Abstract

Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this large-portfolio study suggests a new condition on the reinsurance pricing regime which is crucial for the results obtained. One or two-layer contracts now become optimal for both risk-adjusted surplus and the risk over expected surplus ratio, but there is no second layer when portfolios are large or when reinsurance prices are below some threshold. Simple approximations of the optimum portfolio are considered, and their degree of degradation compared to the optimum is studied which leads to theoretical degradation rates as the number of policies grows. The theory is supported by numerical experiments which suggest that the shape of the claim severity distributions may not be of primary importance when designing an optimal reinsurance program. It is argued that the approach can be applied to Conditional Value at Risk as well.

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  • Erik B{o}lviken & Yinzhi Wang, 2019. "Optimal reinsurance for risk over surplus ratios," Papers 1912.04086, arXiv.org.
    • Handle: RePEc:arx:papers:1912.04086
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    References listed on IDEAS

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    1. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
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    4. Chi, Yichun, 2012. "Reinsurance Arrangements Minimizing the Risk-Adjusted Value of an Insurer's Liability," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 529-557, November.
    5. Yinzhi Wang & Erik B{o}lviken, 2019. "How much is optimal reinsurance degraded by error?," Papers 1912.04175, arXiv.org.
    6. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    7. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
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    1. Yinzhi Wang & Erik B{o}lviken, 2019. "How much is optimal reinsurance degraded by error?," Papers 1912.04175, arXiv.org.

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