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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 ›› 2019, Vol. 36 ›› Issue (5): 557-577.doi: 10.3969/j.issn.1005-3085.2019.05.007

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考虑通货膨胀和多个风险资产的 DC 型养老金的最优策略：市场完备化框架（英）

王丽媛,  陈志平,  李宗欣   

  1. 西安交通大学数学与统计学院，西安  710049
  • 收稿日期:2018-12-11 接受日期:2019-06-27 出版日期:2019-10-15 发布日期:2019-12-15
  • 基金资助:
    国家自然科学基金(11735011;11571270)；世界一流大学和中央大学特色发展指导基金(PY3A058).

Optimal Strategy with Multiple Risky Assets for DC Pension Plans under Inflation: a Market Completion Framework

WANG Li-yuan,  CHEN Zhi-ping,  LI Zong-xin   

  1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2018-12-11 Accepted:2019-06-27 Online:2019-10-15 Published:2019-12-15
  • Supported by:
    The National Natural Science Foundation of China (11735011; 11571270); the World-Class Universities and the Characteristic Development Guidance Funds for the Central Universities (PY3A058).

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摘要： 本文在不完全市场下研究了 DC 型养老金的连续时间最优投资问题．我们考虑了通货膨胀风险，这个因素非常重要但却在很多研究中被忽略了．与很多通常的模型不同的是，我们的模型以最大化实际终期财富的期望效用为目标，并且可以同时处理多个风险资产．通过减少布朗运动的维数使其与风险资产的数目相等，我们在完备市场下得到了一个辅助问题．应用随机动态规划方法，我们推导出相应的 HJB 方程，并在幂效用函数下求得了问题的显式解．最后，为了更好地理解模型结果，我们进行了一系列数值实验来说明模型主要参数对最优策略的影响．

关键词: DC 型养老金计划, 通货膨胀风险, 市场完备化, 随机动态规划, HJB 方程

Abstract: The continuous-time optimal investment problem for a defined contribution (DC) pension plan under an incomplete market is considered in this paper. We take into account the inflation risk which is important but neglected in most studies. Different from many usual models, the proposed model maximizes the expected utility of the actual terminal wealth and can cope with multiple risky assets. By reducing the dimension of the underlying Brownian motions to equal to the number of risky assets, we formulate an auxiliary problem under a complete market. Applying the stochastic dynamic programming method, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation, and obtain the explicit solution under the power utility function. Finally, in order to better understand our results, numerical experiments are carried out to illustrate the effects of main parameters on the optimal strategy.

Key words: DC pension plan, inflation risk, market transformation, stochastic dynamic programming, HJB equation

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