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.

我们提出了基于CANN框架的新型交叉-sectional和纵向索赔计数模型，该框架结合了由Mario Wüthrich和Michael Merz提出的经典精算模型（如广义线性模型）和神经网络。我们的模型使用著名的对数线性索赔计数回归模型来处理经典回归部分，并使用多层感知器（MLP）来处理描述每个投保人驾驶行为的遥测汽车驾驶数据。此外，我们还提出了一种使用多变量负二项分布训练CANN模型的方法。我们的结果表明，与依赖手工特征工程的对数线性模型相比，CANN模型表现出更好的性能。

基于遥感的精算神经网络用于横向和纵向索赔数据