Insurance Risk Premium Development with Model Risk
Kim, Minkun · Dublin City University Open Access Institutional Repository (Dublin City University) · 2025
Accurate risk premium prediction is critical for competitiveness and growth in general insurance business. Traditional approaches focus on clustering risks into well-defined groups to improve prediction accuracy, but practical challenges such as poorly defined risk classes and unexpected model risks complicate this process. This thesis tackles diverse model risks in risk premium prediction using a Bayesian framework. Unlike classical actuarial methods that rely solely on data, Bayesian models incorporate parameter knowledge, offering flexibility in handling erroneous data issue. We leverage this advantage to link Bayesian parametric/ nonparametric frameworks with state-of-art strategies for managing incomplete data issues, such as Missingness at Random (MAR) and Non-Differential Berkson (NDB) mismeasurement. Additionally, we address other key analytical challenges, including heterogeneity, convolution, and scalability. The first part of this thesis focuses on Bayesian parametric frameworks, comparing Bayesian partial pooling with traditional error correction method such as Simulation Extrapolation (SIMEX). The second part extends to the Bayesian nonparametric (BNP) framework, investigating the efficiency of Bayesian parameter-free clustering while addressing incomplete data using techniques such as data augmentation and Gustafson correction. We develop a hybrid Dirichlet Process Mixture (DPM) model and compare it with Bayesian hierarchical models and other classical actuarial approaches. The originality of this thesis lies in leveraging existing state-of-the-art approaches and pushing the boundaries of their applicability to a broader analytical framework, encompassing challenges such as heterogeneity, convolution error, scalability, missingness, and mismeasurement. Based on the combined use of Bayesian parametric and nonparametric models trained on multiple insurance datasets, a critical insight from our study is that correction performance depends on the alignment between two conditional variances in the Gustafson framework—one conditioned on the true covariate and the other on the chosen covariate to approximate the true covariate. We introduce the concept of a scaling factor for the first time to measure this alignment, applying it in calibrating the MCMC simulations. Overall, we believe that this thesis enhances the practical application of Bayesian tools for actuaries. Key innovations include: 1. Integrating data augmentation and Gustafson correction with Bayesian predictive modeling frameworks, leveraging unique prior knowledge of variance in the correction process. 2. Introducing log-normal and log-skewnormal convolution techniques for risk premium modeling, enhancing theoretical reliability. 3. Marking the first instance of integrating advanced Bayesian techniques with scalable methodologies tailored for risk premium prediction.