Constrained portfolio optimization with discrete variables: An algorithmic method based on dynamic programming

Portfolio optimization is one of the most important issues in financial markets. In this regard, the more realistic are assumptions and conditions of modelling to portfolio optimization into financial markets, the more reliable results will be obtained. This paper studies the knapsack-based portfolio optimization problem that involves discrete variables. This model has two very important features; achieving the optimal number of shares as an integer and with masterly efficiency in portfolio optimization for high priced stocks. These features have added some real aspects of financial markets to the model and distinguish them from other previous models. Our contribution is that we present an algorithm based on dynamic programming to solve the portfolio selection model based on the knapsack problem, which is in contrast to the existing literature. Then, to show the applicability and validity of the proposed dynamic programming algorithm, two case studies of the US stock exchange are analyzed.