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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (1): 23-37.doi: 10.3969/j.issn.1005-3085.2021.01.003

• • 上一篇    下一篇

指数保费原理中风险保费的变点推断

章   溢1,   温利民2,   李志龙3,4   

  1. 1- 江西师范大学财政金融学院，南昌  330022
    2- 江西师范大学数学与统计学院，南昌   330022
    3- 海南师范大学数学与统计学院，海口  571158
    4- 海南师范大学大数据科学与智慧教育重点实验室，海口  571158
  • 收稿日期:2018-11-28 接受日期:2019-05-17 出版日期:2021-02-15 发布日期:2021-04-15
  • 通讯作者: 温利民 E-mail: wlmjxnu@163.com
  • 基金资助:
    国家自然科学基金 (71761019)；江西省自然科学基金 (20202BABL201001).

Change Point Inferences of Risk Premium under the Exponential Premium Principle

ZHANG Yi1,   WEN Li-min2,  LI Zhi-long3,4   

  1. 1- School of Finance, Jiangxi Normal University, Nanchang 330022
    2- School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
    3- School of Mathematics and Statistics, Hainan Normal University, Haikou 571158
    4- Key Laboratory of Big Data Science and Smart Education, Hainan Normal University, Haikou 571158
  • Received:2018-11-28 Accepted:2019-05-17 Online:2021-02-15 Published:2021-04-15
  • Contact: L. Wen. E-mail address: wlmjxnu@163.com
  • Supported by:
    The National Natural Science Foundation of China (71761019); the Natural Science Foundation of Jiangxi Province (20202BABL201001).

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摘要： 保费定价是指精算师根据风险的分布特征确定一个合理的保费的过程．为了提高保险公司的竞争力，制定的保费必须科学合理且与保单风险相匹配．然而，由于风险因素的复杂性，保单风险的结构性变化常导致保费发生改变，保费的变点检测是保险公司重要的问题之一．本文建立了指数保费的变点检测模型，基于变点统计推断方法，提出了检测风险保费结构变点的统计量，并给出了保费变点位置的估计．进而，证明了估计量的大样本性质和收敛速度．最后，利用数值模拟的方法对统计量的收敛性进行了验证，比较了不同位置导致的保费变点检测的精度差异．本文的研究能为保险公司的保费定价和变点检测提供决策参考．

关键词: 指数保费原理, 风险保费, 变点, 假设检验, 相合性

Abstract: Premium pricing refers to the process by which an actuary determines a reasonable premium based on the distribution characteristics of the risk. In order to improve the competitiveness of insurance companies, the premiums must be scientific and reasonable and matches the policy risks. However, due to the complexity of risk factors, structural changes in policy risk often lead to changes in premiums, and the detection of premiums is one of the important issues for insurance companies. In this paper, the change point detection model of the exponential premium principle is established. Based on the statistical inference methods in change point theory, the statistic of detecting the change point of the risk premium is proposed, and the estimation of the change point position of the premium is given. Furthermore, the large sample properties and the convergence speed of the estimator are proved. Finally, the numerical simulation method is used to verify the convergence of the statistics, and the accuracy difference of the premium change detection caused by different positions is compared. The method presented in this paper can provide reference value and basis for the insurance company's premium pricing and change detection.

Key words: exponential premium principle, risk premium, change point, hypothesis test, consistency

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