Actuaries use predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. State-of-the-art statistical and machine learning methods are not well equipped to handle hierarchically structured risk factors with a large number of levels. In this paper, we demonstrate the data-driven construction of an insurance pricing model when hierarchically structured risk factors, contract-specific as well as externally collected risk factors are available. We examine the pricing of a workers' compensation insurance product with a hierarchical credibility model [Jewell, W. S. (1975). The use of collateral data in credibility theory: A hierarchical model. Laxenburg: IIASA], Ohlsson's combination of a generalized linear and a hierarchical credibility model [Ohlsson, E. (2008). Combining generalized linear models and credibility models in practice. Scandinavian Actuarial Journal 2008(4), 301–314] and mixed models. We compare the predictive performance of these models and evaluate the effect of the distributional assumption on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. For our case-study the Tweedie distribution is well suited to model and predict the loss cost on a contract. Moreover, incorporating contract-specific risk factors in the model improves the predictive performance and the risk differentiation in our workers' compensation insurance portfolio.

精算师使用预测建模技术来评估合同的损失成本，作为可观察风险特征的函数。最先进的统计和机器学习方法不足以处理具有大量级别的分层结构风险因素。在本文中，我们演示了当分层结构的风险因素、特定于合同的风险因素以及外部收集的风险因素可用时，数据驱动的保险定价模型的构建。我们用分层可信度模型研究了工人赔偿保险产品的定价[Jewell, WS (1975)。抵押数据在可信度理论中的使用：层次模型。Laxenburg：IIASA]，Ohlsson 的广义线性模型和分层可信度模型的组合 [Ohlsson，E. (2008)。在实践中结合广义线性模型和可信度模型。斯堪的纳维亚精算杂志 2008 (4), 301–314] 和混合模型。我们比较这些模型的预测性能，并通过将线性混合模型与 Tweedie 广义线性混合模型进行比较来评估分布假设对目标变量的影响。对于我们的案例研究，Tweedie 分布非常适合建模和预测合同的损失成本。此外，在模型中纳入特定于合同的风险因素可以提高我们工人赔偿保险组合的预测性能和风险差异化。