A Simple Method for Solving Multiperiod Mean-Variance Asset-Liability Management Problem

This paper introduces the Lagrange duality method for solving the multiperiod mean-variance (M-V) asset-liability management (ALM) problem. First, Using the Lagrange multiplier technique, the original problem is turned into a multi-period unconstrained Optimal Control Problem (OCP) that is separable in the sense of dynamic programming. Then the dynamic programming approach is applied to solve the OCP. Finally, closed form expressions of the efficient investment strategy and the M-V efficient frontier are obtained.