华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 4: 60 - 69

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.04.007

数学

Pareto风险模型中分位数保费的贝叶斯估计

  • 魏斯怡 ,
  • 章溢 ,
  • 温利民
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  • 1. 江西师范大学 数学与信息科学学院, 南昌330022; 2. 江西师范大学 计算机信息工程学院，南昌 330022

收稿日期: 2015-06-24

  网络出版日期: 2016-09-29

基金资助

国家自然科学基金 (71361015); 江西省自然科学基金 (20142BAB201013); 江西师范大学研究生创新基金 (2014010654); 教育部人文社科基金 (15YJC910010, 14YJC630085)

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The Bayes estimation of quantile premium in Pareto risk model

  • WEI Si-yi ,
  • ZHANG Yi ,
  • WEN Li-min
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  • 1. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Computer and Information Engineering, Jiangxi Normal University, Nanchang 330022, China

Received date: 2015-06-24

  Online published: 2016-09-29

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摘要

分位数保费原理是非寿险精算中的一种重要的保费原理, 在保险中有重要的应用. 建立分位数保费原理的Pareto风险模型, 通过引入损失函数, 结合一些统计技巧, 给出了分位数保费原理下风险保费的贝叶斯保费、贝叶斯估计、极大似然估计以及分位数估计. 进而, 讨论了这些估计的统计性质. 最后, 利用数值模拟的方法比较了这些估计的平均误差.

关键词： 分位数保费原理; Pareto风险模型; 相合性; 渐近正态性

本文引用格式

魏斯怡 , 章溢 , 温利民 . Pareto风险模型中分位数保费的贝叶斯估计[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(4) : 60 -69 . DOI: 10.3969/j.issn.1000-5641.2016.04.007

Abstract

Quantile premium principle is one of the important premium principles in non-life insurance actuarial science, which is widely used in insurance practice. The Pareto risk model for quantile premium principle was established by introducing a class of loss function, and using some statistical techniques, and some estimates of risk premium including Bayes premium, Bayes estimate, maximum likelihood estimation and quantile estimation under the quantile premium principle were given. Furthermore, the statistical properties of these estimations were discussed. Finally, the mean error of these estimations were compared by using numerical simulation method.

Key words： quantile premium principle; Pareto risk model; consistency; asymptotical normality

参考文献

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