报告时间：2022年3月16日

               上午10:00-11:00

报告地点：腾讯会议

（会议ID：545 569 162）

报告嘉宾：张艺赢

报告主题：基于非齐次风险的满意信度理论方法

报告摘要

Satisficing Credibility for Heterogeneous Risks

As one of the earliest crucial applications of Bayesian statistics, credibility theory (see Bühlmann and Gisler, 2006) 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 L2-optimal truncation point can be determined in an ad hoc manner, but the derivation of its general explicit formula is difficult. In this talk, 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 in an asymptotic sense. A comprehensive numerical study also illuminates that with the aid of this newly obtained truncation point, the corresponding semi-linear credibility formula outperforms the classical Bühlmann model.

个人简介

张艺赢，南方科技大学数学系助理教授，博士生导师。2012年及2015年分别在兰州大学数学与统计学院获得理学学士和硕士学位。2018年9月在香港大学统计与精算学系获得精算学方向哲学博士学位， 2018年10月至2019年1月在鲁汶大学和阿姆斯特丹大学进行学术访问。2019年1月至2021年8月在南开大学统计与数据科学学院工作，任助理教授。2021年8月加入南方科技大学数学系，任tenure-track助理教授。目前的主要研究领域包括风险管理与保险精算、应用概率及可靠性理论与统计。主要研究兴趣包括最优再保险、信度理论、系统性风险、风险测度、相依风险模型、随机序理论及随机比较、可靠性分析及系统可靠性设计与优化。已在保险精算主要期刊IME、SAJ、ASTIN Bulletin和NAAJ，以及运筹管理领域主流期刊EJOR、RESS和NRL等杂志发表多篇学术研究论文。