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基于跳跃扩散死亡率模型的新型年金定价及其风险评估

胡仕强, 龙宇   

  1. 浙江财经大学金融学院, 杭州 310018
  • 收稿日期:2022-07-05 修回日期:2022-10-20 发布日期:2023-05-18
  • 通讯作者: 胡仕强, Email:crazyrobert3478@126.com
  • 基金资助:
    教育部人文社会科学研究规划基金项目(20YJA790025), 浙江省教育厅科研项目(Y202044525)资助课题.

胡仕强, 龙宇. 基于跳跃扩散死亡率模型的新型年金定价及其风险评估[J]. 系统科学与数学, 2023, 43(4): 929-946.

HU Shiqiang, LONG Yu. Mortality-Linked Annuity Pricing and Its Risk Assessment Based on a Jump Diffusion Stochastic Mortality Model[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(4): 929-946.

Mortality-Linked Annuity Pricing and Its Risk Assessment Based on a Jump Diffusion Stochastic Mortality Model

HU Shiqiang, LONG Yu   

  1. Finance School, Zhejiang University of Finance and Economics, Hangzhou 310018
  • Received:2022-07-05 Revised:2022-10-20 Published:2023-05-18
由于各个年龄段的人口死亡率呈现出的明显下降趋势,依赖静态生命表的传统精算方法已经无法实现年金收支上真正的精算等价, 这无疑会严重影响到保险公司的风险管理和稳健运营. 因此文章尝试从死亡率的随机建模和死亡率衍生产品创新的角度来准确度量风险并进而厘清风险的权责和分摊. 首先, 文章将建立带跳跃过程的随机死亡率模型, 以中国实际死亡率的历史数据, 对模型参数进行最大似然估计, 并运用\;Bootstrap 方法对参数估计的精确程度进行检验; 其次, 文章在产品设计层面探讨动态的支付调整, 即在年金产品中嵌入一个欧式死亡率期权,给予保险公司根据真实死亡率调整赔付额度的权利.文章的研究结果表明新型年金能够有效分散长寿风险, 提高承保双方的效用,对促进商业年金的发展具有重要的现实意义和参考价值.
The projection of human mortality has always been a fundamental subject in actuarial research. Because of the clear downward trend of mortality rate in all ages, traditional actuarial fairness which rely on static life tables have difficult in meeting the requirements of insurance product pricing and risk assessment, what’s more, the risk management and sound operation of insurance companies will be seriously affected. Consequently, this article will try to explore the coping strateg from the perspective of stochastic modeling of mortality and innovation of mortalityderived products. First, this paper will build a stochastic modeling of mortality with a jump process, and use the Bootstrap method and maximum likelihood estimation method to estimate the parameters in the model based on the actual mortality data of China from 1995 to 2019. Secondly, this article innovates in product design: Embedding a European option of mortality in annuity products which grants insurance companies the right to adjust the compensation when actual mortality deviates too much from the predicted mortality. The results show that the embedded mortality options can effectively disperse longevity risk and has important practical significance and reference value to promote the development of commercial annuity.

MR(2010)主题分类: 

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