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2013 Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process
Hao Chang, Xi-min Rong
J. Appl. Math. 2013(SI26): 1-8 (2013). DOI: 10.1155/2013/348059

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.

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Hao Chang. Xi-min Rong. "Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process." J. Appl. Math. 2013 (SI26) 1 - 8, 2013. https://doi.org/10.1155/2013/348059

Information

Published: 2013
First available in Project Euclid: 7 May 2014

zbMATH: 06950626
MathSciNet: MR3124615
Digital Object Identifier: 10.1155/2013/348059

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI26 • 2013
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