• 数学 •

### 基于分层贝叶斯模型的损失准备金估计

1. 1. 江西财经大学 统计学院, 南昌 330013;
2. 江西师范大学 统计系, 南昌 330022
• 收稿日期:2017-09-29 出版日期:2019-01-25 发布日期:2019-01-24
• 通讯作者: 温利民,男,教授,研究方向为保险精算.E-mail:wlmjxnu@163.com E-mail:wlmjxnu@163.com
• 作者简介:章溢,女,博士研究生,研究方向为数理统计.E-mail:yizi85820@163.com.
• 基金资助:
国家自然科学基金（71761019，71361015）；江西省自然科学基金（20171ACB21022）；江西省人文社科基金（15WTZD10）

### Estimation of loss reserves based on a hierarchical bayesian model

ZHANG Yi1, LIU Zhi-qiang2, ZOU Si-si2, WEN Li-min2

1. 1. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;
2. Department of Statistics, Jiangxi Normal University, Nanchang 330022, China
• Received:2017-09-29 Online:2019-01-25 Published:2019-01-24

Abstract: Traditional loss reserve models are mainly based on aggregate loss triangles, in which the entries are obtained by summations of individual loss data. The summation procedures inevitably cause wastage of information contained in the raw individual data. Though this method is simple, it results in a larger error in the estimate of loss reserves. Individual loss reserve models emerging in recent years have failed to consider dependencies between policies. This article assumes the existence of certain common random effects between policies in the same accident year. Thus, a hierarchical bayesian model is built for individual data loss reserves. Using the ideas of credibility theory, we get the credibility estimate of loss reserves in each accident year, and thus the total reserve. In addition, the estimation of structural parameters and development factors are discussed. And the statistical properties are derived for those estimators of structural parameters. Finally, a numerical example is given to show the calculations with our estimators, and simulations are done to compare the mean square of reserve estimator between an individual loss model and an aggregate data model.