Dynamic mean-variance model with borrowing constraint under the constant elasticity of variance process

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. © 2013 hao chang and xi-min rong.