Optimal Reinsurance under VaR and CVaR Risk Measures: A Simplified Approach
Optimal Reinsurance under VaR and CVaR Risk Measures: A Simplified Approach
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DOI：
10.2143/ast.41.2.2136986
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Yichun Chi;K. S. Tan
中科院分区：
文献类型：
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作者：
Yichun Chi;K. S. Tan
在本文中，我们通过在风险价值（VaR）和条件风险价值（CVaR）标准下最小化保险公司的总风险暴露来研究两类最优再保险模型。我们假设再保险保费是按照期望值原则计算的。最优再保险政策的显式解是通过让出损失函数导出的，并且通用性不断增强。更准确地说，我们正式确定，在 VaR 最小化模型下，（i）止损再保险在递增凸分让损失函数类别中是最优的； (ii) 当分出损失函数和留存损失函数的约束都放宽为递增函数时，具有上限的止损再保险被证明是最优的； (iii) 最后，在一般递增和左连续保留损失函数的集合下，截断止损再保险被证明是最优的。相反，在 CVaR 风险衡量下，止损再保险始终是最优的。这些结果表明，基于 VaR 的再保险模型对于分出损失函数和保留损失函数的约束都很敏感，而相应的基于 CVaR 的再保险模型则相当稳健。
In this paper, we study two classes of optimal reinsurance models by minimizing the total risk exposure of an insurer under the criteria of value at risk (VaR) and conditional value at risk (CVaR). We assume that the reinsurance premium is calculated according to the expected value principle. Explicit solutions for the optimal reinsurance policies are derived over ceded loss functions with increasing degrees of generality. More precisely, we establish formally that under the VaR minimization model, (i) the stop-loss reinsurance is optimal among the class of increasing convex ceded loss functions; (ii) when the constraints on both ceded and retained loss functions are relaxed to increasing functions, the stop-loss reinsurance with an upper limit is shown to be optimal; (iii) and finally under the set of general increasing and left-continuous retained loss functions, the truncated stop-loss reinsurance is shown to be optimal. In contrast, under CVaR risk measure, the stop-loss reinsurance is shown to be always optimal. These results suggest that the VaR-based reinsurance models are sensitive with respect to the constraints imposed on both ceded and retained loss functions while the corresponding CVaR-based reinsurance models are quite robust.