Stochastic Loss Reserving: Statistical and Machine Learning Approaches

Abstract

Loss reserving refers to the prediction of future claims arising from existing policies. Accurate reserve forecasts are essential for insurer solvency, profitability, and regulatory compliance. Contemporary solvency regimes increasingly require not only point estimates but also explicit quantification of uncertainty, motivating the use of stochastic reserving models that provide predictive distributions. This thesis develops three novel stochastic models for loss reserving using aggregated run-off triangle data. The first project introduces a Bayesian bi-directional self-exciting threshold autoregressive model that captures local dependence across both accident and development year directions. Thresholds are treated as random variables, and posterior inference is conducted using both discretised approximation and adaptive Markov Chain Monte Carlo methods, enabling coherent uncertainty quantification. The second project focuses on modelling global development patterns across the run-off triangle. It develops a parsimonious Bayesian model based on flexible gamma basis functions, in which both the location and scale structures are modelled directly as functions of accident and development indices. This formulation captures smooth development patterns while avoiding excessive parameterisation. The third project explores a machine learning approach that relaxes structural assumptions further by combining a bi-directional long short-term memory network with a mixture density network output layer. This model exploits both local neighbourhood information and global positional structure to produce probabilistic forecasts without manually specified dynamics. Together, these three models provide progressively flexible frameworks for stochastic loss reserving, offering improved uncertainty quantification while remaining suitable for the practical constraints of real-world insurance data.