It is well-known that Excess-of-Loss reinsurance has more marketability than Stop-Loss reinsurance, though Stop-Loss reinsurance is the most prominent setting discussed in the optimal (re)insurance design literature. We point out that optimal reinsurance policy under Stop-Loss leads to a zero insolvency probability, which motivates our paper. We remedy this peculiar property of the optimal Stop-Loss reinsurance contract by investigating the optimal Excess-of-Loss reinsurance contract instead. We also provide estimators for the optimal Excess-of-Loss and Stop-Loss contracts and investigate their statistical properties under many premium principle assumptions and various risk preferences, which, according to our knowledge, have never been investigated in the literature. Simulated data and real-life data are used to illustrate our main theoretical findings.

中文翻译：

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重新审视最佳超额损失合约


众所周知，超额损失再保险比止损再保险更具适销性，尽管止损再保险是最佳（再）保险设计文献中讨论的最突出设置。我们指出，止损下的最佳再保险政策导致零破产概率，这激发了我们的论文。我们通过研究最佳超额损失再保险合同来补救最佳止损再保险合同的这一特殊特性。我们还为最佳超额损失和止损合约提供估算器，并研究它们在许多溢价原则假设和各种风险偏好下的统计特性，根据我们的知识，这些在文献中从未研究过。模拟数据和真实数据用于说明我们的主要理论发现。