数学与统计学院学术报告[2023] 022号

(高水平大学建设系列报告793号)

报告题目: Credibility theory under the least squared relative loss function

报告人：雍尧棣，博士后，南方科技大学数学系

报告时间：2023.04.20 11:00am-12:00pm

讲座地点：汇星楼（科技楼）501

报告内容：In many areas of actuarial science, credibility theory plays a significant role in insurance pricing. Determination of individuals' premiums is crucial to insurance companies as the premiums shall secure a stable income for the insurer and reflect the risk features of insureds. The classical credibility model attains the best linear estimator for the hypothetical mean under the quadratic loss criterion. Nonetheless, when the claim observations from different insureds exhibit a noticeable magnitude difference, the classical Bühlmann model might be severely distracted under the quadratic loss criterion and thus cannot provide a good predicted value for the insured's future claims. As a remedy, the present work proposes a new credibility theory under the least squared relative loss (LSRL) function tailored for such scenarios. Starting with a simple credibility model, the explicit credibility estimator and its corresponding mean squared error are established. Some of its properties are presented compared with the classical Bühlmann model both in theory and practical usage. We then extend it to the Bühlmann-Straub framework under LSRL function and present its non-parametric estimators, with which a practical example is applied for showing its performance. This is a joint work with Xiaobai Zhu (The Chinese University of Hong Kong).

报告人简历：雍尧棣，南方科技大学数学系博士后。2022年9月获得香港大学统计及精算学博士学位，2022年11月至2023年1月在南方科技大学数学系学术访问。主要研究方向为保险精算，信度理论与寿险定价。目前共发表SCI学术论文近10篇，其中多篇发表于应用数学领域知名期刊Journal of Mathematical Analysis and Applications、Journal of Computational and Applied Mathematics等。

　 数学与统计学院

                                                2023年04月17日