In actuarial research a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking and capital management. The loss cost is typically viewed to follow a compound distribution where the summation of the severity variables is stopped by the frequency variable. A challenging issue in modeling such outcomes is to accommodate the potential dependence between the number of claims and the size of each individual claim. In this article we introduce a novel regression framework for compound distributions that uses a copula to accommodate the association between the frequency and the severity variables and, thus, allows for arbitrary dependence between the two components. We further show that the new model is very flexible and is easily modified to account for incomplete data due to censoring or truncation. The flexibility of the proposed model is illustrated using both simulated and real data sets. In the analysis of granular claims data from property insurance, we find substantive negative relationship between the number and the size of insurance claims. In addition, we demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.

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关联变量复合分布的回归及其在总保险索赔建模中的应用

在精算研究中，特别重要和重要的任务是预测单个风险的损失成本，以便在各种保险业务（如承保，费率制定和资本管理）中做出明智的决定。通常认为损失成本遵循复合分布，其中严重性变量的总和被频率变量停止。在对此类结果进行建模时，一个具有挑战性的问题是要适应索赔数量和每个索赔大小之间的潜在依存关系。在本文中，我们为复合分布引入了一种新颖的回归框架，该框架使用copula来适应频率和严重性变量之间的关联，从而允许两个组件之间的任意依赖。我们进一步表明，新模型非常灵活，可以轻松修改以解决由于审查或截断而导致的不完整数据。使用仿真和真实数据集说明了所提出模型的灵活性。在对财产保险的详细索赔数据进行分析时，我们发现保险索赔的数量和规模之间存在实质性的负相关关系。此外，我们证明了忽略频率-严重性关联可能导致保险业务中的决策偏差。我们发现保险索赔的数量和规模之间存在实质性的负相关关系。此外，我们证明了忽略频率-严重性关联可能导致保险业务中的决策偏差。我们发现保险索赔的数量和规模之间存在实质性的负相关关系。此外，我们证明了忽略频率-严重性关联可能导致保险业务中的决策偏差。