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

Hao Chang and Xi-min Rong

Journal of Applied Mathematics, 2013, vol. 2013, 1-8

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:348059

DOI: 10.1155/2013/348059

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