Nonlinear mixed-effect compartmental model in loss reserving

• Main Author: Ng, Wei Siang
• Format: Thesis
• Published: 2021
• Subjects: QA Mathematics; QC Physics
• Online Access: http://eprints.sunway.edu.my/2394/

The Bayesian hierarchical compartmental loss reserving model is an one of a kind model under the loss reserving context in the actuarial society. In this research, the model will be reformulated with some improvements on the Bayesian assumptions to increase its practical usage in the industry. First of all, the Markov chain Monte Carlo methods are used to approximate the posterior distribution of the parameters. In particular, the No-U-Turn sampling (NUTS) is replacing the Gibbs sampling method to reduce the computation time and resources. Furthermore, several convergence diagnostics are performed, supported with descriptive statistics and visualisations after sampling is done. These checkings can avoid questionable decision making based on the sampling chains as it makes the posterior inference scientifically and statistically defensible. Besides, multiple loss triangle datasets contain only a single entity with different lines of business are fitted to the models. In conclusion, the application of NUTS gives better results and the analysis of multiple datasets with the model further prove the nonlinear mixed-effect compartmental loss reserving model can fit dataset with a different line of business. In addition, the Bayesian reformulation and the convergence diagnostics give a better understanding on the application and formulation of the Bayesian loss reserving model.