Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

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

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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).

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

CLC Number: