Multi-period Mean-variance Portfolio Selection with Practical Constraints using Heuristic Genetic Algorithms

Since Markowitz proposed the mean-variance (MV) formulation in 1952, it has been used to configure various portfolio selection problems. However Markowitz's solution is only for a single period. Multi-period portfolio selection problems have been studied for a long time but most solutions depend on various forms of utility function, which are unfamiliar to general investors. Some works have formulated the problems as MV models and solved them analytically in closed form subject to certain assumptions. Unlike analytical solutions, genetic algorithms (GA) are more flexible because they can solve problems without restrictive assumptions. The purpose of this paper is to formulate multi-period portfolio selection problems as MV models and solve them by GA. To illustrate the generality of our algorithm, we implement a program by Microsoft Visual Studio to solve a multi-period portfolio selection problem for which there exists no general analytical solution.