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Mathematical Problems in Engineering
Volume 2016, Article ID 2391849, 18 pages
Research Article

Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

1School of Mathematics, Lanzhou City University, Lanzhou 730070, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
3Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China
4Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received 8 December 2015; Revised 2 April 2016; Accepted 4 April 2016

Academic Editor: Reza Jazar

Copyright © 2016 Jingyun Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a portfolio selection problem for a defined contribution (DC) pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV). Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB) equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.