Multiperiod mean-variance portfolio model with constraints

The mean-variance optimization, known as the Markowitz portfolio, is a cornerstone of modern portfolio theory. This model helps investors create mathematically optimal portfolios. While the original Markowitz model provides investors with an optimal portfolio for a single period, we extend this model to multiple periods. This extension allows investors to perform asset re-balancing more than once, which is more relevant to real-world practice. In this study, we consider the portfolio optimization problems without constraint and some constraint cases, namely no bankruptcy and bounded leverage. We solve the portfolio optimization problems using the methods of pre-commitment, multi-stage strategy, and Karush-Kuhn-Tucker (KKT). We perform numerical simulations to construct portfolio efficient frontiers with various parameters. Based on numerical simulations, we discovered that our proposed method is consistent with the result of [2].