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：本文提出了基于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次数模型。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。这种模型混合方式产生了一个包含经典回归模型和神经网络部分的两组件模型。CANN模型充分发挥了两组件的优势：从经典模型中获得稳健基础与可解释性，同时利用神经网络捕捉复杂关系与交互的灵活性与能力。在我们提出的模型中，经典回归部分采用熟知的对数线性索赔次数回归模型，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投保驾驶员驾驶行为的远程信息处理车辆行驶数据。除针对横截面数据的泊松分布与负二项分布外，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。通过此方法，我们引入了一个考虑同一投保人保单间相关性的纵向模型。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模型展现出更优的性能。