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金融工程研究中心学术报告:Credibility theory under the least squared relative loss function



报告地点:腾讯会议 538-779-644

嘉宾简介:张艺赢,南方科技大学数学系助理教授,博士生导师。20189月获得香港大学精算学博士学位,后赴鲁汶大学和阿姆斯特丹大学学术访问,2019.1-2021.8在南开大学统计与数据科学学院工作,任助理教授,20218月加入南方科技大学数学系,任助理教授。主要研究方向为风险管理与保险精算、应用概率与统计及可靠性理论,目前共发表SCI/SSCI/EI论文60余篇,研究成果主要发表在保险精算四大顶级期刊Insurance: Mathematics and EconomicsASTIN BulletinNorth American Actuarial JournalScandinavian Actuarial Journal,运筹学与管理科学领域权威期刊European Journal of Operational Research Naval Research Logistics,工程技术领域顶级期刊Reliability Engineering & System Safety。获中国优选法统筹法与经济数学研究会工业工程分会2022年学术交流年会最佳论文奖。20152018年获得香港政府博士生全额奖学金 (HKPFS)2019年入选天津市131创新型人才培养工程第三层次,2021年入选南方科技大学鹏城孔雀特聘岗位。担任中国商业统计学会理事,国际综合类SCIE期刊Symmetry客座编辑。主持完成天津市自然科学基金青年项目一项,现主持国家自然科学基金青年项目一项及广东省基础与应用基础研究面上项目一项。

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讲座概要: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 Buhlmann 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 Buhlmann model both in theory and practical usage. We then extend it to the Buhlmann-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 Yaodi Yong (SUSTech) and Xiaobai Zhu (CUHK).


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