Deep neural networks have become an important tool for use in actuarial tasks, due to the significant gains in accuracy provided by these techniques compared to traditional methods, but also due to the close connection of these models to the Generalized Linear Models (GLMs) currently used in industry. Whereas constraining GLM parameters relating to insurance risk factors to be smooth or exhibit monotonicity is trivial, methods to incorporate such constraints into deep neural networks have not yet been developed. This is a barrier for the adoption of neural networks in insurance practice since actuaries often impose these constraints for commercial or statistical reasons. In this work, we present a novel method for enforcing constraints within deep neural network models, and we show how these models can be trained. Moreover, we provide example applications using real-world datasets. We call our proposed method ICEnet to emphasize the close link of our proposal to the individual conditional expectation (ICE) model interpretability technique.

翻译：深度神经网络已成为精算任务中的重要工具，这得益于这些技术相比传统方法在准确性上的显著提升，同时也因其与行业内当前使用的广义线性模型（GLMs）存在紧密关联。虽然对有关保险风险因子的GLM参数施加平滑性或单调性约束十分简单，但将此类约束引入深度神经网络的方法尚未被开发。这构成了神经网络在保险实践中推广应用的障碍，因为精算师常因商业或统计原因强制施加这些约束。在本研究中，我们提出了一种在深度神经网络模型中施加约束的新方法，并展示了如何训练这些模型。此外，我们使用真实世界数据集提供了应用示例。我们将所提出的方法命名为ICEnet，以强调本方案与个体条件期望（ICE）模型可解释性技术之间的紧密联系。