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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 ›› 2015, Vol. 32 ›› Issue (3): 337-347.doi: 10.3969/j.issn.1005-3085.2015.03.003

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通胀和奈特不确定下的养老金最优投资研究

梁  勇,   费为银,   姚远浩,   芮亚运   

  1. 安徽工程大学数理学院，安徽 芜湖 241000
  • 收稿日期:2014-09-11 接受日期:2015-03-05 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (71171003).

Study on Optimal Portfolio for Defined Contribution Pension with Inflation and Knightian Uncertainty

LIANG Yong,   FEI Wei-yin,   YAO Yuan-hao,   RUI Ya-yun   

  1. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000
  • Received:2014-09-11 Accepted:2015-03-05 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (71171003).

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摘要： 本文研究了奈特不确定下带有通胀的固定供款型养老基金的最优投资问题．首先，利用伊藤公式推导考虑通胀的消费篮子价格动力学方程．其次，在奈特不确定下，建立代理人的财富动态方程，同时根据代理人对不同的公司存在不同的含糊程度，利用随机控制理论刻画代理人的期望效用，得到HJB方程，通过求解HJB方程给出代理人最优投资的显式解．最后，对结果进行数值分析，定量分析了含糊和通胀因素对代理人最优投资策略的影响．

关键词: 含糊厌恶, 通胀, 固定供款, 随机控制, 最优投资策略

Abstract:

In this paper, we study an optimal investment strategy for defined contribution pension plan with inflation under Knightian uncertainty. Firstly, we obtain the dynamics of consumer-basket-price with inflation by using It\^o formula. Secondly, we establish the wealth dynamic equation for an agent, and characterize the agent's expected utility function by the stochastic control theory, where the agent has different levels of ambiguity aversion to different companies. Thirdly, we get the HJB equation, from which we obtain the explicit form solutions of the optimal investment strategy. Finally, we analyze the impacts of the ambiguity and the inflation on the optimal investment strategy of an agent through a numerical simulation.

Key words: ambiguity aversion, inflation, defined contribution, stochastic control, optimal investment strategy

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