Exact method for generating efficient solutions to constrained portfolio assets selection

International audienceThe problem of portfolio selection is one of the most popular areas in Finance. In this work, we will rely on the theory of Harry Markowitz, and the works of Ralph Steuer] for a quad-lin bi-objective mixed integer model. Next, we will propose an exact method for its resolution based on the conjugate gradient, and the cutting efficiency of Chergui et al. as well as new exploration strategy of problems generated in the branches. The proposed algorithm will also be applied to different cardinality constraint conditions, for different market indices

An iterative method for finding the efficient frontier for a cardinality constrained portfolio assets selection

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An exact method for multiple objective mixed-integer linear programming problem

International audienceIn this article, we present an exact method to find all efficient solutions of the multi-objective mixed-integer linear programming problem (MOMILP). Based on the branching process and by using an efficient cut to find at each iteration a new efficient solution (if it exists), the proposed algorithm is able to identify all the efficient solutions of the MOMILP problem in a finite number of iterations

An empirical study to find the optimal number of security in portfolio selection problem

International audiencePortfolio selection problem is one of the most important issues in finance. It had a lot of enthusiasm from the scientific community these last decades specially after the work of the father of modern portfolio theory Harry Markowitz. The aim of this work is to find the optimal number of securities in portfolio selection problem, to get the best efficient frontier. A statistical study is conducted on a different markets. We consider issues of selection of securities under cardinality constraints, as a mixed model bi-objective variable we will solve afterwards with an exact method. Experiments are performed with major market indices, such as the Hang Seng, DAX100, FTSE 100, S&P 100, Nikkei, S&P 500 and Nasdaq

Exact method for solving bi-objective cardinality constrained portfolio selection problem

International audienceIn finance, the portfolio optimization problem made a significant progress after Markowitz’s seminal who develop the modern portfolio theory, which stipulates that a portfolio selection problem consists of minimizing the risk represented by the variance and maximizing the ex- pected return. In this work, a bi-objective mixed integer quadratic model is presented, holding notice of real world constraints, which are the constraints on number of selected assets, called "cardinality constraints". For its resolution, we propose an exact method based on the steepest gradient and a new exploration strategy of problems generated at each step. The main idea of this method is to compute the maximum point by considering exclusively the return function obtained by solving a Mixed Integer Linear problem (MILP). Then, after adding a cut effe- ciency that takes into account the risk function, the augmented problem must be solved until finding the minimum of the risk function. This proposed method is validate using some major market indices, such as the Hang Seng, DAX100, FTSE 100, S&P 100, Nikkei, S&P 500 and Nasdaq and by using real data sets involving up to 2196 assets. The results show that this method finds Pareto optimal solutions in a reasonable time

An iterative method for solving a bi-objective constrained portfolio optimization problem

International audienceIn this work, we consider the problem of portfolio optimization under cardinality and quantity constraints. We use the standard model of mean-variance in its bi-objective form which is presented here as a bi-objective quadratic programming problem under cardinality and quantity constraints. This problem is NP-hard, which is why the majority of methods proposed in the literature use metaheuristics for its resolution. In this paper, we propose an iterative method for solving constrained portfolio optimization problems. Experiments are performed with major market indices, such as the Hang Seng, DAX, FTSE, S&P 100, Nikkei, S&P 500 and Nasdaq using real-world datasets involving up to 2196 assets. Comparisons with two exact methods and a meta-heuristic are performed. These results show that the new method allows to find efficient portfolio fronts in reasonable time. Keywords Cardinality and Quantity constraints · Cardinality portfolio selection · Bi-objective programming · Mixed integer programming · Steepest descent method · Pascoletti-Serafini method Mathematics Subject Classification (2000) 90C29 · 90C90 · 90C11 · 90B50 · 91B28 M. Bezoui University M'hamed Bougara of Boumerdes, 35000. LaROMad

A Distributed Algorithm to Find Boundaries of Connected Components of a Euclidean Graph

National audienceEuclidean graphs are widely used in various fields, such as computing sciences, space exploration, neural networks, etc. In many cases, the majority of these graphs have vertices randomly deployed. This random aspect can make the graph divided into disjoint connected components with a topology that needs to be built. We propose a new technique to find the connected components and their boundaries using only connectivity information between a vertex and their neighbors. We show by an extensive simulation that the algorithm gives good results with a random generation of Wireless Sensors Networks

A new hybrid method to maximize the lifetime of coverage in IoT networks

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A New Distributed Algorithm for Finding Dominating Sets in IoT Networks under Multiple Criteria

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A game theory approach to solve linear bi-objective programming problems

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