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Mathematical Problems in Engineering
Volume 2013, Article ID 974098, 11 pages
Research Article

Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2School of Science, Tianjin University, Tianjin 300072, China
3School of Business, Tianjin University of Finance and Economics, Tianjin 30022, China

Received 21 July 2013; Accepted 3 October 2013

Academic Editor: Fazal M. Mahomed

Copyright © 2013 Hao Chang 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 an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.