Portfolio selection problem: main knowledge and models (A systematic review)

The challenge in portfolio optimization lies in creating a collection of assets that attains a target expected returnwhile mitigating risk. This problem is often framed as an optimization task, specifically Mean Variance Optimization (MVO). MVO involves formulating an objective function, typically quadratic, that is contingent on the composition of the portfolio, and linear constraints that represents the portfolio's asset allocation restriction. Several improvements have been proposed, such as adding constraints to MVO or using alternative risk measures. As a result, even though MVO model remains the most widely studied type of portfolio optimization, different types of portfolio optimization models, risk/return measurements and constraints have been suggested and used since its invention. In this work, we delve into the various risk and return measures, constraints, and mathematical models commonly used in portfolio optimization.We discuss the key risk measures employed in portfolio optimization, including the Sharpe ratio, beta, maximum drawdown and others, We explore the constraints commonly applied in portfolio optimization. Furthermore, we delve into the mathematical models utilized in portfolio optimization. Then, we emphasize the interplay between risk and return measures, constraints, and mathematical models in portfolio optimization. By providing a comprehensive overview of risk and return measures, constraints, and mathematical models, this work aims to enhance the understanding of portfolio optimization techniques and facilitate informed decisionmaking in the field of investment management. To illustrate different knowledge and models, several experiments were conducted on well-known real data portfolios.