Continuous-Time Mean-Variance Model with Uncertain Exit Time

By using Lagrange duality methods, this paper studies the continuous-time mean-variance portfolio selection problem with uncertain exit time. Firstly, the original mean-variance problem is turned into a stochastic optimal control problem containing Lagrange multiplier. Secondly, the corresponding Hamilton- Jacobi-Bellman HJB equation is solved analytically. Thirdly, the efficient investment strategy and efficient frontier for the original mean-variance problem is explicitly obtained. Finally, a numerical example illustrates the results in this paper.