文澜金融论坛（第257期）

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.

主讲人介绍：

高光远，中国人民大学统计学院副教授。主要研究领域包括非寿险准备金评估方法、贝叶斯统计、车险定价模型、车联网大数据分析、copulas、死亡率预测模型等。研究成果发表在《ASTIN Bulletin》《Insurance: Mathematics and Economics》《Machine Learning》等国际期刊，在Springer出版著作《Bayesian Claims Reserving Methods in Non-life Insurance with Stan》。参与编著多本教材，建设慕课《金融数学》《非寿险精算学》。主持国家自科青年项目、Society of Actuaries科研项目等，参与国家社科重大项目等。