Time-Consistent Investment Strategy for DC Pension Plan with Stochastic Salary Under CEV Model

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• 作者：Danping Li ; Ximin Rong ; Hui Zhao
• 关键词：Constant elasticity of variance model ; defined contribution pension plan ; mean ; variance criterion ; stochastic salary ; time ; consistency investment strategy
• 刊名：Journal of Systems Science and Complexity
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：29
• 期：2
• 页码：428-454
• 全文大小：688 KB
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• 作者单位：Danping Li (1)
  Ximin Rong (1) (2)
  Hui Zhao (1)
  
  1. School of Science, Tianjin University, Tianjin, 300072, China
  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067

文摘

This paper aims to derive the time-consistent investment strategy for the defined contribution (DC) pension plan under the mean-variance criterion. The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance (CEV) model. Compared with the geometric Brownian motion model, the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile. The authors assume that the contribution to the pension fund is a constant proportion of the pension member’s salary. Meanwhile, the salary is stochastic and its volatility arises from the price process of the risky asset, which makes the proposed model different from most of existing researches and more realistic. In the proposed model, the optimization problem can be decomposed into two sub-problems: Before and after retirement cases. By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman (HJB) systems, the authors derive the time-consistent strategies and the corresponding value functions explicitly. Finally, numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.