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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 ›› 2021, Vol. 38 ›› Issue (6): 778-796.doi: 10.3969/j.issn.1005-3085.2021.06.003

• • 上一篇    下一篇

DC 型养老基金在多维相依风险资产中的最优配置

孙景云1,2,   郭精军1,   赵  煜1   

  1. 1. 兰州财经大学统计学院,兰州 730020
    2. 兰州财经大学甘肃经济发展数量分析研究中心,兰州  730020
  • 出版日期:2021-12-15 发布日期:2022-02-15
  • 基金资助:
    国家自然科学基金 (71701084; 71961013; 72061020);甘肃省自然科学基金 (21JR1RA280);甘肃省高等学校创新能力提升项目 (2019A-060);兰州财经大学丝绸之路经济研究院项目 (JYYY201705).

Optimal Asset Allocation for a DC Pension Fund in the Market with Multiple Dependent Risky Assets

SUN Jingyun1,2,   GUO Jingjun1,   ZHAO Yu1   

  1. 1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020
    2. Center for Quantitative Analysis of Gansu Economic Development, Lanzhou University of Finance and Economics, Lanzhou 730020
  • Online:2021-12-15 Published:2022-02-15
  • Supported by:
    The National Natural Science Foundation of China (71701084; 71961013; 72061020); the Natural Science Foundation of Gansu Province (21JR1RA280); the Innovation Ability Promotion Project for the Higher Education Institutions of Gansu Province (2019A-060); the Project of Silk Road Economic Research Institute in Lanzhou University of Finance and Economics (JYYY201705).

摘要:

考虑了缴费确定型养老基金在参与者退休前累积阶段的最优资产配置问题。假定金融市场中多个风险资产的价格由于遭受市场系统性风险的冲击而产生共同的跳跃现象,因而用相依跳扩散模型来刻画,并假定参与者退休前的收入过程也满足一个跳扩散过程。以最小化退休时刻养老基金账户与预期投资目标之间的期望平方损失为优化准则,利用随机动态规划方法,分别获得了最优投资策略及值函数的解析形式,并给出验证定理及其证明过程。最后通过数值算例发现,风险资产价格及参与者收入过程中的跳跃参数、养老基金管理者的盈余偏好和预期投资目标均对最优投资策略及值函数产生较大的影响。

关键词: 缴费确定型, 相依跳扩散, 平方损失, Hamilton-Jacobi-Bellman 方程

Abstract:

We consider an optimal asset allocation problem for a defined contribution pension fund in the accumulation phase before the participant retired. It is assumed that the prices of $n$ risky assets suffer a common jump phenomenon because of the impact of market systematic risk. So the prices of the risky assets are modeled with dependent jump-diffusion processes. In addition, we suppose that the income process of the participant satisfies a jump-diffusion process before she retired. To minimize the expected square loss between the pension fund account and the expected investment target at the time of retirement, the stochastic dynamic programming method is adopted, and the closed-forms of the optimal investment strategy and the value function are obtained, a verification theorem and its proof are also provided. Finally, through some numerical examples, we find that the jump parameters in the price process of risky asset and participants' income process, the earnings preference of pension fund managers and the expected investment objective process all have significant influence on the optimal investment strategy and the value function.

Key words: defined contribution, dependent jump-diffusion, quadratic loss, Hamilton-Jacobi-Bellman equation

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