In this article, we consider a multi-period portfolio optimization problem, which is an extension of the single-period mean-variance model. We discuss several formulations of the objective function, constraints and coupling relationships.
Multi-period portfolio optimization is a natural extension of the mean-variance optimization (MVO) model developed by Harry Markowitz in 1952. The goal is to find the dynamic asset allocation policy by considering inter-temporal effects such as rebalancing costs, trading impacts, time-varying constraints, price trends, etc. Since such models include feedback features, we might think that they are commonly used by the asset management industry. However, while mean-variance optimization was very successful among investors and portfolio managers, multi-period optimization is mainly an academic research field.
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