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Journal of Applied Mathematics
Volume 2013, Article ID 348059, 8 pages
Research Article

Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2School of Science, Tianjin University, Tianjin 300072, China

Received 24 April 2013; Revised 17 September 2013; Accepted 1 October 2013

Academic Editor: Rung Ching Chen

Copyright © 2013 Hao Chang and Xi-min Rong. 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.


This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.