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, issue 1

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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https://doi.org/10.1155/2013/348059

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:348059

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