In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

中文翻译：

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根据 CVAR 风险衡量和 VajDA 条件，从保险公司和再保险公司的角度来看最佳再保险

在本文中，我们研究了最优再保险合同，该合同使保险人损失的条件风险价值 (CVaR) 和再保险人损失在分出损失函数类别上的凸组合最小化，使得保留损失函数增加并且割让的损失函数满足 Vajda 条件。在满足风险负荷和凸保序性质的一类再保险保费原则中，得到最优解。我们的研究结果表明，对于一般再保险保费原则，最优分出损失函数采用五个相互关联的部分的形式，如果再保险保费原则中增加更多属性，它们可以进一步简化为四个相互关联的部分。最后，