In this project, we propose a flexible regression model that incorporates random effects to account for latent, heterogeneous risks observed in large insurance portfolios.
The proposed model, called Mixed LRMoE, is shown to have the potential to capture any latent structure of unobserved random effects, making it a powerful tool not only in insurance loss modelling but also more general applications where random effects are traditionally used.
As an illustration, we apply the model to a large, multi-year automobile insurance portfolio. We develop an effective variational algorithm for approximated estimation of model parameters and inference of random effects. We also illustrate the superior performance of the model by differentiating risky drivers from safer ones and by calculating a posteriori premia that reasonably reflect the heterogeneity in drivers' latent, unobserved risks.
Fung, T. C., & Tseung, S. C. (2022). Mixture of experts models for multilevel data: Modelling framework and approximation theory. Submitted for review. Preprint available at arXiv:2209.15207.
Tseung, S. C., Chan, I. W., Fung, T. C., Badescu, A. L., & Lin, X. S. (2022). A posteriori risk classification and ratemaking with random effects in the mixture-of-experts model. Submitted for review. Preprint available at arXiv:2209.15212.
Presentation: University of Toronto Statistics Graduate Student Research Day, May 25, 2022
Presentation: 2022 Annual Meeting of the Statistical Society of Canada, May 31, 2022