  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.
