The 257th Wenlan Financial Forum

Abstract:
We consider the situation when the number of claims is not observed and a Tweedie's compound Poisson model is fitted to pure premium. Currently, there are two different model fitting approaches: a single generalized linear model (GLM) with homogeneous dispersion and a double generalized linear model (DGLM) with heterogeneous dispersion. Although the DGLM approach facilitates the heterogeneous dispersion, its soundness relies on the accuracy of the saddlepoint approximation, which is poor when the exposure is small and the proportion of zero claims is large. For both approaches, the power variance parameter is estimated by considering the profile likelihood, which is computational expensive. We propose a new model fitting approach using the EM algorithm, where the number of claims is treated as unobserved latent data. The proposed method addresses the heterogeneous dispersion without the saddlepoint approximation, and the power variance parameter is estimated during the model fitting. A simulated example shows that our approach is superior than the two competing approaches.

Speaker Introduction:
Guangyuan Gao is an associate professor at the School of Statistics, Renmin University of China. His main research areas include non-life insurance reserve assessment methods, Bayesian statistics, auto insurance pricing models, big data analysis of the Internet of Vehicles, copulas, mortality prediction models, etc. The research results have been published in international journals such as ASTIN Bulletin, Insurance: Mathematics and Economics, Machine Learning, and the book "Bayesian Claims Reserving Methods in Non-life Insurance with Stan" which was published in Springer. He also participated in the compilation of several textbooks and the construction of the MOOCs "Financial Mathematics" and "Non-Life Insurance Actuarial Science".