An important problem in the banking and insurance industries is that of pricing risk. The two come together when a bank buys insurance to decrease the impact of potential operational risk losses. The price of such insurance hinges on the computation of risk premiums, which involves the computation of expected values with respect to the loss distribution. When the empirical data set is not large and loss distributions are inferred from the data, a large sample dependence of the premiums on the data is to be expected. The maximum entropy-based methodologies offer model-free, non- parametric procedures to determine probability densities from empirical data with high precision. At the same time, they provide us with a framework within which to study how the sample dependence is transferred from the data to the premiums via the density. It is the aim of our paper to show how this can be done.

中文翻译：

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风险溢价的样本依赖

银行业和保险业的一个重要问题是定价风险。当银行购买保险以减少潜在操作风险损失的影响时，两者结合在一起。此类保险的价格取决于风险溢价的计算，其中涉及与损失分布相关的预期值的计算。当经验数据集不大并且从数据推断损失分布时，可以预期保费对数据的大样本依赖性。基于最大熵的方法提供了无模型、非参数化的程序，以高精度从经验数据中确定概率密度。同时，它们为我们提供了一个框架，可以在该框架内研究样本依赖性如何通过密度从数据转移到保费。