二元贝叶斯聚合风险模型中保费的后验厘定  

The Posterior Ratemaking of Premium in Binary Bayesian Collective Risk Model

作　　者：章溢 ZHANG Yi(School of Finance,Jiangxi Normal University,Nanchang,330022,China;School of Finance,Jiangxi University of Finance and Economics,Nanchang,330013,China)

机构地区：[1]江西师范大学财政金融学院,南昌330022 [2]江西财经大学金融学院,南昌330013

出　　处：《应用概率统计》2022年第2期237-252,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:71761019);江西省教育厅科学技术研究项目(批准号:GJJ200304)资助.

摘　　要：将索赔额区分为大额索赔和小额索赔,在方差相关保费原理下研究了二元贝叶斯聚合风险模型中风险保费的贝叶斯估计.结论显示,风险的条件期望和条件方差都能表达为样本函数和聚合保费的加权形式,其中权重满足\信度因子"的性质.进而,证明了贝叶斯估计的强相合性和渐近正态性.最后,利用数值模拟的方法验证了贝叶斯估计的大样本性质.In the Collective risk model,the claim amount is divided into large claims and small claims.Under the variance-related premium principle,the Bayesian estimation of the risk premium in the binary Bayesian collective risk model is derived.The conclusion shows that both the conditional expectation and conditional variance parts of risk premium can be expressed as a weighted form of sample function and aggregate premium,where the weight satis es the property of"credibility factor".Furthermore,the strong consistency and asymptotic normality of Bayesian estimation is proved.Finally,the method of numerical simulation is used to verify the large sample properties of Bayesian estimation.

关 键 词：聚合风险模型 风险保费 方差相关保费原理 信度估计 渐近正态性 

分 类 号：O211.9[理学—概率论与数理统计]