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

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  • Hao Chang
  • Xi-min Rong

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.

Suggested Citation

  • Hao Chang & Xi-min Rong, 2013. "Dynamic Mean‐Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:348059
    DOI: 10.1155/2013/348059
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    References listed on IDEAS

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    6. Christina Paxson, 1990. "Borrowing Constraints and Portfolio Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(2), pages 535-543.
    7. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
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