In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performa...

In this paper we tackle the optimal portfolio selection problem (PSP). Many research has been made around this subject mainly in two ways, whether extending the Markowitz model by taking into account real-world constraints (floor-ceiling, class and cardinality) or introducing different risk measures like semivariance, value at risk, absolute desviation, etc. Here, we present the preliminary res...

The construction of the best combination of investment instruments (investment portfolio) is a principal goal of investment policy. This is an optimization problem: select the best portfolio from all admissible portfolios. To approach this problem we have to choose the selection criterion first. The seminal paper of Markowitz [8] opened a new era in portfolio optimization. The paper formulated ...

Introduction One of the basic problems of applied finance is the optimal selection of stocks by conflicting objective of maximizing future return and minimizing investment risk. The first systematic treatment of this dilemma is the mean variance approach proposed by Markowitz. Markowitz combined the optimization and probability theory to solve the dilemma. In Markowitz’s mean variance model, th...

Portfolio optimization requires the minimal risk with certain expected return. The risk structure of securities, such as their exposure to countries, industrial sectors, or commodity/factor, have to be characterized, and then the optimal weights of securities in a portfolio can be determined to minimize the exposure of the portfolio to any specific risk factor. Typically, the risk factors are n...

I develop a two market agent-based model to study how global portfolio managers affect global financial crises and stability. The Markowitz model is extended by incorporating several insights from behavioral finance. Simulation results of an agent-based version of the Markowitz model reveal that global financial crises do not occur when global managers are added to the model. However, when risk...

Since the 1960s, lots of scholars had begun to research in the portfolio selections based on the theory of mean-variance of Markowitz portfolio and relevant methods. All of these studies are under certainly of the assumption term, and then the researchers can get efficient set of portfolio selection. However, alone with the finance environment increasing of complexity, it is becoming more compl...