Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process. (17th November 2013)

• Record Type: Journal Article
• Authors: Chang, Hao; Rong, Xi-min
• Other Names: Chen Rung Ching Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-11-17
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/348059
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.