Pareto风险模型中分位数保费的贝叶斯估计

doi:10.3969/j.issn.1000-5641.2016.04.007

华东师范大学学报(自然科学版)

Pareto风险模型中分位数保费的贝叶斯估计

魏斯怡^[1] , 章溢^[1,2] , 温利民^[1]

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 出版日期:2016-07-25 发布日期:2016-09-29
通讯作者: 温利民, 男, 教授, 研究方向为金融经济、保险精算. E-mail: wlmjxnu@163.com.
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)

The Bayes estimation of quantile premium in Pareto risk model

WEI Si-yi^[1], ZHANG Yi^[1,2], WEN Li-min^[1]

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:2015-06-24 Online:2016-07-25 Published:2016-09-29

摘要/Abstract

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

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

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), doi: 10.3969/j.issn.1000-5641.2016.04.007.

WEI Si-yi, ZHANG Yi, WEN Li-min. The Bayes estimation of quantile premium in Pareto risk model[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2016.04.007.

参考文献

[1] ASIMIT V A, BADESCU A, VERDONCK T. Optimal risk transfer under quantile-Based risk measures [J]. Social Science Electronic Publishing, 2013, 53(1): 252-265.

[2] 欧阳资生. 厚尾分布的极值分位数估计与极值风险测度研究 [J]. 数理统计与管理, 2008, 27(1): 70-75.

[3] 谢佳利, 杨善朝, 梁鑫. VaR~样本分位数估计的偏差改进 [J]. 数量经济技术经济研究, 2008, 12: 139-148.

[4] GELMAN A, CARLIN J B, STERN H S, et al. Bayesian Data Analysis [M]. New York: Chapman-Hall, 1995.

[5] SZEGO G. Measures of risk [J]. European Journal of Operational Research, 2005, 163: 5-19.

[6] DENUIT M, DHAENE J, GOOVAERTS M, et al. Actuarial Theory for Dependent Risks [M]. [S.l.]: John Wiley Sons Ltd, 2005.

[7] RAMSAY C M. A solution to the ruin problem for pareto distributions [J]. Insurance: Mathematics and Economics, 2003, 33(1): 109-116.

[8] ALBRECHER H, KORTSCHAK D. On ruin probability and aggregate claim representations for pareto claim size distributions [J]. Insurance: Mathematics and Economics, 2009, 45(3): 362-373.

[9] BRAZAUSKAS V, KLEEFELD A. Robust and efficient fitting of the generalized pareto distribution with actuarial applications in view [J]. Insurance: Mathematics and Economics, 2009, 45(3): 424-435.

[10] HE H, ZHOU N, ZHANG R. On estimation for the Pareto distribution [J]. Statistical Methodology, 2014, 21(11): 49-58.

[11] TUDOR C A. Chaos expansion and asymptotic behavior of the Pareto distribution [J]. Statistics and Probability Letters, 2014, 91(3): 62-68.

[12] FAHIDY T Z. Applying pareto distribution theory to electrolytic powder production [J]. Electrochemistry Communications, 2011, 13(3): 262-264.

[13] DIXIT U J, NOOGHABI M J. Efficient estimation in the pareto distribution with the presence of outliers [J]. Statistical Methodology, 2011, 8(4): 340-355.

[14] HARRIS C M. The pareto distribution as a queue service discipline [J]. Operational Research, 1968, 16(2): 307-313.

[15] ARNOLD B C. Pareto distribution [M]. [S.l.]: International Co-operative Publishing House, 1983.

[16] STEINDL J. Random processes and the growth of firms [M]. [S.l.]: Hafner Pub Co, 2004.

[17] HAGSTROEM K G. Remarks on pareto distributions [J]. Skandinavisk Aktuarietidskrift, 1960(1/2): 59-71.

[18] 茆诗松, 王静龙, 濮晓龙. 高等数理统计 [M]. 北京: 高等教育出版社, 2006.

[19] WALKER A M. On the asymptotic behavior of posterior distributions [J]. Journal of the Royal Statistical Society Series B(Methodological), 1969, 31(1): 80-88.

[20] BUHLMANN H, GISLER A. A Course in Credibility Theory and its Applications [M]. Amsterdam: Springer, 2005.

[21] 温利民. 信度估计的理论与方法 [M]. 北京: 科学出版社, 2012.

[22] PAN M, WANG R, WU X. On the consistency of credibility premiums regarding esscher principle [J]. Insurance Mathematics and Economics, 2008, 42(1): 119-126.

[23] 郑丹, 章溢, 温利民. 具有时间变化效应的信度模型 [J]. 江西师范大学学报, 2012(3): 249-252.

[24] 方婧, 章溢, 温利民. 聚合风险模型下的信度估计 [J]. 江西师范大学学报, 2012(6): 607-611.

Pareto风险模型中分位数保费的贝叶斯估计

The Bayes estimation of quantile premium in Pareto risk model

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