In this paper, we obtain an optimal reinsurance contract explicitly in the form of excess-of-loss with a limit when the risk measure is Range-Value-at-Risk. Then we study optimal reinsurance with model uncertainty, where the uncertainty set contains a greatest element in the sense of stochastic order. Furthermore, we study the Stackelberg game in reinsurance with model uncertainty. In order to illustrate how our findings can be applied in practice to determine the optimal reinsurance contract, we perform an empirical study using the Wisconsin Local Government Property Insurance Fund dataset. Tweedie distributions are fit to the building and contents loss amounts from the property fund, and used to determine the optimal loading factor, and reinsurance contract corresponding to the loading factor. From the analysis, we discover that some policies have more recoveries from the optimal reinsurance contract than the premium paid, while others have smaller recoveries than the premium.

在本文中，当风险度量为 Range-Value-at-Risk 时，我们明确地以超额损失的形式获得了一个最优再保险合同。然后我们研究具有模型不确定性的最优再保险，其中不确定性集合包含随机顺序意义上的最大元素。此外，我们研究了具有模型不确定性的再保险中的 Stackelberg 博弈。为了说明我们的发现如何在实践中应用以确定最佳再保险合同，我们使用威斯康星州地方政府财产保险基金数据集进行了实证研究。Tweedie 分配适用于财产基金中的建筑物和内容物损失金额，并用于确定最佳加载因子，以及与加载因子相对应的再保险合同。从分析来看，