In this tutorial paper we introduce different approaches to Markowitz portfolio optimization, and we show how to solve such problems in MATLAB, R and Python using the MOSEK optimization toolbox for MATLAB, the Rmosek package, and the MOSEK Python API, respectively. We first consider conic formulations of the basic portfolio selection problem, and we then discuss more advanced models for transac...

Many recent theoretical developments in the field of machine learning and control have rapidly expanded its relevance to a wide variety of applications. In particular, a variety of portfolio optimization problems have recently been considered as a promising application domain for machine learning and control methods. In highly uncertain and stochastic environments, portfolio optimization can be...

Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our ap...

In this paper, a constrained mean-variance model is constructed for the portfolio optimization problems. The model is a mixed quadratic integer programming problem, and it is too hard to solve by using the traditional optimal algorithms. The purpose of this paper is to use a heuristic algorithm to solve this problem. Combined with the differential evolution strategy, a new hybrid artificial bee...

In an intensifying competition banks are forced to develop and implement enterprise wide integrated risk-return management systems. Financial risks have to be limited and managed from a bank wide portfolio perspective. Risk management rules must be accomplished from internal and regulatory points of view. Expected returns need to be maximized subject to these constraints, leading to a generaliz...

This work presents a new prediction-based portfolio optimization model that can capture short-term investment opportunities. We used neural network predictors to predict stocks’ returns and derived a risk measure, based on the prediction errors, that have the same statistical foundation of the mean-variance model. The efficient diversification effects holds thanks to the selection of predictors...

Standard market risk optimization tools, based on assumptions of normality, are ineffective for credit risk. In this paper, we develop three scenario optimization models for portfolio credit risk. We first create the trade risk profile and find the best hedge position for a single asset or obligor. The second model adjusts all positions simultaneously to minimize the regret of the portfolio sub...