A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but challenges remain in developing models that can (i) allow covariates to flexibly impact different aspects of the conditional distribution, (ii) integrate developments in machine learning and AI to maximise the predictive power while considering (i), and, (iii) maintain a level of interpretability in the model to enhance trust in the model and its outputs, which is often compromised in efforts pursuing (i) and (ii). We tackle this problem by proposing a Distributional Refinement Network (DRN), which combines an inherently interpretable baseline model (such as GLMs) with a flexible neural network-a modified Deep Distribution Regression (DDR; Li et al., 2019) method. Inspired by the Combined Actuarial Neural Network (CANN; Schelldorfer and W{\''u}thrich, 2019), our approach flexibly refines the entire baseline distribution. As a result, the DRN captures varying effects of features across all quantiles, improving predictive performance while maintaining adequate interpretability. Using both synthetic and real-world data, we demonstrate the DRN's superior distributional forecasting capacity. The DRN has the potential to be a powerful distributional regression model in actuarial science and beyond.

翻译：精算建模中的一个关键任务涉及对损失分布特性的建模。经典（分布）回归方法如广义线性模型（GLMs；Nelder and Wedderburn, 1972）被广泛使用，但在开发满足以下要求的模型时仍面临挑战：（i）允许协变量灵活影响条件分布的不同方面；（ii）结合机器学习和人工智能领域的最新进展，在考虑（i）的同时最大化预测能力；以及（iii）保持模型一定程度的可解释性以增强对模型及其输出的信任——这在追求（i）和（ii）的过程中常被削弱。我们通过提出分布精化网络（DRN）来解决这一问题，该网络将本质可解释的基线模型（如GLMs）与灵活的神经网络——一种改进的深度分布回归（DDR；Li et al., 2019）方法相结合。受组合精算神经网络（CANN；Schelldorfer and Wüthrich, 2019）的启发，我们的方法灵活地精化整个基线分布。因此，DRN能够捕捉特征在所有分位数上的不同效应，在保持足够可解释性的同时提升预测性能。通过使用合成数据和真实数据，我们证明了DRN在分布预测方面的卓越能力。DRN有潜力成为精算学及其他领域一种强大的分布回归模型。