Multi-period Mean-Variance Model with Uncertain Exit Time

Abstract

By using Lagrange duality methods, this paper studies the multi-period mean-variance portfolio selection problem with uncertain exit time. Firstly, according to Lagrange duality theorem, we turn the original mean-variance problem into a multi-period optimization problem, which contains a Lagrange multiplier with separability and so can be solved by dynamic programming approach. Secondly, we obtain the analytical solution to the corresponding basic equation, and explicitly obtain the efficient investment strategy and efficient frontier for the original mean-variance problem.