Abstract：The method of credibility theory plays a critical role in various research areas of actuarial science. Among others, the hypothetical mean and process variance are two quantities that convey crucial information to insurance companies when determining premiums for the insureds. The classical simple Bühlmann model charges premiums by applying a linear combination of the mean of past claims and the population mean, which is proven the best estimator of the hypothetical mean under the mean squared loss criterion. Enlightened by the prestigious mean-variance premium principle, we propose a credibility approach to estimating the linear combination of hypothetical mean and process variance under the mean quadratic loss function. It is found that our proposed estimator consists of several parts involved with the linear form of observations and their quadratic terms, as well as some quantities representing population information. Several numerical illustrations are carried out to demonstrate the performance of the estimator.  Meanwhile, a spin-off result is found and utilized to compare with the classical simple Bühlmann model and the q-credibility model. The non-parametric estimators of structural quantities are also provided for ease of its practical usage, yielding the empirical credibility estimator.

报告人简介：雍尧棣，香港大学统计与精算系在读博士生. 2015及2018年在重庆大学分别获得学士、硕士学位, 专业为统计学。2018年9月至今在香港大学攻读博士学位, 专业为精算学。主要研究方向为保险精算, 信度理论与统计。目前共发表SCI论文6篇, 研究成果主要发表在《Journal of Industrial & Management Optimization》、《Journal of Computational and Applied Mathematics》以及《Journal of Mathematical Analysis and Applications》等期刊上。