教育部人文社科重点研究基地中央财经大学中国精算研究院学术活动
精算论坛第129期讲座-Udi E. Makov、Runhuan Feng (2月26日)
报告一：
报告题目：Actuarial applications ofnon-informative prior distributions and intrinsic discrepancy loss functions
报告时间：2018年2月26日 上午10:00—11:00
报告人：UdiE. Makov 教授（以色列University of Haifa 精算研究中心主任）
摘要：
One of the mainactuarial problems, with particular relevance to the insurance industry, is theevaluation of fair premium. The Bayesian approach provides a specific solutionwhich minimizes the posterior expected loss associated with the underlyingrisk. This would require a choice of a prior distribution and a loss functionwhich would have a direct impact on the nature of the outcome. Different rulesfor selecting a prior distribution and loss function have been recommended inthe literature. In this study we adopt the objective Bayesian inferenceapproach which combines an objective prior distribution -which is designed toexpress absence of information about the quantity of interest with respect tothe information inherent in the data -and an intrinsic discrepancy lossfunction-which is the inherent loss function arising only from the underlyingdistribution or model, without any subjective considerations. The combined useof objective prior distribution and the intrinsic discrepancy loss functionprovides us with an intrinsic objective Bayesian point estimator of thequantity of interest.
The intrinsicobjective Bayesian point estimation allows an objective evaluation of the fairpremium - objective in the sense of being fully dependent on the available dataand the underlying model without subjective influence. The aim of this talk isto explore the intrinsic discrepancy loss function (IDLF), the intrinsicobjective Bayesian point estimator and its approximation for some popularmodels which have significant relevance to actuarial science. We willinvestigate hitherto partially or fully unexplored models in this novelcontext.
In the firstpart of the talk, we discuss the intrinsic objective Bayesian estimation of themean of the Gamma distribution and the mean of the Poisson distribution,typically used for assessing claim severity and claim frequency, respectively.We provide the IDLF of the Gamma model, which is fully unexplored in thiscontext, and for the latter we explore the intrinsic objective Bayesian pointestimators and its approximation, based on IDLF and the Jeffrey's priordistribution. Additionally, we illustrate the methodology with simulated dataand compare our outcomes with the Bayes estimator, which is the posterior meanbased on quadratic (squared error) loss function and Jeffrey's priordistribution.
As ageneralization, we study the intrinsic objective Bayesian estimation of themean of the Tweedie family, which is a subclass of reproductive exponentialdispersion family (EDF), a reach family with wide applications. We provide theIDLF of the EDF and of members of the Tweedie family. Furthermore, we explorethe intrinsic objective Bayesian point estimator and its approximation for themean value of the Tweedie family based on the IDLF and the Jeffrey's priordistribution. Additionally, we carry a numerical study to illustrate the methodologyin the context of the Inverse Gaussian model, which is fully unexplored in thisnovel context, and which is useful to insurance contracts.
Finally, weinvestigate the intrinsic Bayesian point estimation for the mean of the Tweediefamily which relies on conjugate prior distribution and the IDLF. We derive anapproximate intrinsic Bayesian point estimator for the mean value of severalmembers of the family and establish links between the approximate estimatorsand credibility estimators which are typically limited to the quadratic lossfunction. Accordingly, our approach suggests a new tool for evaluating fairpremiums based on past experiences and objective loss function, whichasymptotically coincides with the credibility solution for special cases of thefamily.
报告二：
报告题目：Risk Engineering: fromMathematical Fun to Practical Research
报告时间：2018年2月26日 上午11:00—12:00
报告人：RunhuanFeng 副教授（美国UIUC 精算项目负责人）
摘要：
Naturaldisasters and human-made hazards are inevitable but their consequences need notto be. Engineers respond by designing autonomous vehicles that preventaccidence, making earthquake-proof buildings, developing life saving medicalequipment. We actuaries and financial analysts answer by creating and managinginnovative financial and insurance products to reduce and mitigate thefinancial impact of car accidents, earthquakes, and make healthcare availableto those in dire need.
Thefocus of this talk is to provide an overview of various research topicspertaining to quantitative risk management and engineering of equity-linkedinsurance products and personal retirement planning. It aims to demonstrate themathematical fun with risk management problems as well as to offer a glimpse oftechnical development and challenges arising from these fields.
报告地点：中央财经大学学术会堂南楼506（精算院会议室）
欢迎各位老师和同学积极参加！
