We present a method for constructing and interpreting weighted premium principles. The method is based on modifying the underlying risk distribution in such a way that the risk-adjusted expected value (or premium) is greater than the expected value of some conveniently chosen function of claims, which defines the insurer’s perception of the risk. Under some assumptions on the function of claims, the method produces distortion premium principles. We provide several examples under different assumptions on the claim arrival process and different functions of claims, including record claims and kth record claims.

中文翻译：

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一种构造和解释某些加权高级原理的方法

我们提出一种构造和解释加权保费原则的方法。该方法基于修改基本风险分布的方式，以使风险调整后的期望值（或溢价）大于某些方便选择的索赔功能的期望值，这定义了保险公司对风险的感知。在对索赔功能的某些假设下，该方法产生失真溢价原理。我们在索赔到达过程和索赔功能不同的不同假设下提供了几个示例，包括记录索赔和第k条记录索赔。