We present novel cross-sectional and longitudinal claim count models for vehicle insurance built upon the Combined Actuarial Neural Network (CANN) framework proposed by Mario W\"uthrich and Michael Merz. The CANN approach combines a classical actuarial model, such as a generalized linear model, with a neural network. This blending of models results in a two-component model comprising a classical regression model and a neural network part. The CANN model leverages the strengths of both components, providing a solid foundation and interpretability from the classical model while harnessing the flexibility and capacity to capture intricate relationships and interactions offered by the neural network. In our proposed models, we use well-known log-linear claim count regression models for the classical regression part and a multilayer perceptron (MLP) for the neural network part. The MLP part is used to process telematics car driving data given as a vector characterizing the driving behavior of each insured driver. In addition to the Poisson and negative binomial distributions for cross-sectional data, we propose a procedure for training our CANN model with a multivariate negative binomial (MVNB) specification. By doing so, we introduce a longitudinal model that accounts for the dependence between contracts from the same insured. Our results reveal that the CANN models exhibit superior performance compared to log-linear models that rely on manually engineered telematics features.

翻译：我们提出了基于Mario Wüthrich和Michael Merz提出的组合精算神经网络（CANN）框架的新型车辆保险横截面与纵向索赔计数模型。CANN方法将经典精算模型（如广义线性模型）与神经网络相结合。这种模型融合产生了一个双组件模型，包含经典回归模型部分和神经网络部分。CANN模型充分利用了两组件的优势，既从经典模型获得坚实基础与可解释性，又借助神经网络捕捉复杂关系与交互的灵活性和能力。在我们提出的模型中，经典回归部分采用广为人知的对数线性索赔计数回归模型，神经网络部分则使用多层感知机（MLP）。MLP部分用于处理以向量形式表征每位被保险驾驶员驾驶行为的远程信息处理驾驶数据。除了适用于横截面数据的泊松分布和负二项分布外，我们还提出了一种使用多元负二项分布（MVNB）规范训练CANN模型的流程。通过这种方式，我们引入了一个能处理同一保险人不同保单间依赖关系的纵向模型。研究结果表明，与依赖人工设计远程信息处理特征的对数线性模型相比，CANN模型展现出更优越的性能。