 Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-RiskHaiyan Liu and Tiantian Mao Insurance: Mathematics and Economics, 2022, vol. 107, issue C, 393-417 Abstract: A basic assumption of the classic reinsurance model is that the distribution of the loss is precisely known. In practice, only partial information is available for the loss distribution due to the lack of data and estimation error. We study a distributionally robust reinsurance problem by minimizing the maximum Value-at-Risk (or the worst-case VaR) of the total retained loss of the insurer for all loss distributions with known mean and variance. Our model handles typical stop-loss reinsurance contracts. We show that a three-point distribution achieves the worst-case VaR of the total retained loss of the insurer, from which the closed-form solutions of the worst-case distribution and optimal deductible are obtained. Moreover, we show that the worst-case Conditional Value-at-Risk of the total retained loss of the insurer is equal to the worst-case VaR, and thus the optimal deductible is the same in both cases. Keywords: Value-at-Risk; Conditional Value-at-Risk; Distributional robust reinsurance; Uncertainty; Stop-loss (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:107:y:2022:i:c:p:393-417 DOI: 10.1016/j.insmatheco.2022.09.002 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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