报告简介 Abstract
As one of the earliest crucial applications of Bayesian statistics, credibility theory was first developed for net premium calibration in insurance by optimally combining individual claim history with other those from the whole population; for a century, this research direction has become a major discipline in the interplay among actuarial science, operational research and statistics. Traditionally, for the ease of calibration, the credibility formula is a linear functional of historical observations, which greatly simplifies the underlying computational complexity; yet, its downside is the resulting high sensitivity towards outliers. To remedy this shortcoming, De Vylder (1976) proposed to first transform the observations collected particularly by truncation, and this semi-linear approach was further investigated in Bühlmann and Gisler (2006). Gisler (1980) suggested that the $L^2$-optimal truncation point can be determined in an ad hoc manner, however its general explicit formula is hardly derived. In our present work, to strike a balance between practical usage and mathematical tractability, we focus on heterogeneous risks all coming from possibly different MDAs of the extreme value distributions, which well suffices in practice. By incorporating the satisficing method commonly used in operational research, we close the gap by providing the explicit formula for the aforementioned optimal truncation point up to a slowly varying function of the sample size. A comprehensive numerical study also illuminates that with the aid of this newly obtained truncation point, the corresponding semi-linear credibility formula surpasses in performance the classical Bühlmann model. This is a joint work with Ka Chun Cheung (HKU) and Phillip Yam (CUHK).
嘉宾简介 About the Speaker
张艺赢博士，南开大学统计与数据科学学院助理教授，于2018年在香港大学获得精算学方向哲学博士学位，2015年及2012年分别于兰州大学数学与统计学院分别获得理学硕士学位和学士学位。目前的研究方向主要集中在可靠性理论与统计(协同系统可靠性分析与优化)、风险管理(风险测度、系统风险、风险比较与度量、资金分配)、保险精算（信度理论、最优再保险、个体风险模型）。已发表SCI/SSCI学术论文30余篇，其中包管理学与运筹学领域知名期刊Naval Research Logistics, 保险精算领域三大顶级期刊Insurance: Mathematics and Economics，Scandinavian Actuarial Journal, ASTIN Bulletin
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