An Approach Based on Active Constraint Strategy for Solving The Portfolio Optimization Problem (original) (raw)
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Heuristic algorithms for the portfolio selection problem with minimum transaction lots
European Journal of Operational Research, 1999
The problem of selecting a portfolio has been largely faced in terms of minimizing the risk, given the return. While the complexity of the quadratic programming model due to Markowitz has been overcome by the recent progress in algorithmic research, the introduction of linear risk functions has given rise to the interest in solving portfolio selection problems with real constraints. In this paper we deal with the portfolio problem with minimum transaction lots. We show that in this case the problem of ®nding a feasible solution is, independently of the risk function, NP-complete. Moreover, given the mixed integer linear model, new heuristics are proposed which starting from the solution of the relaxed problem allow to ®nd a solution close to the optimal one. The algorithms are based on the construction of mixed integer subproblems (using only a part of the securities available) formulated using the information obtained from the solution of the relaxed problem. The heuristics have been tested with respect to two disjoint time periods, using real data from the Milan Stock Exchange. Ó
A Local Search Approach to Solve a Financial Portfolio Design Problem
International Journal of Applied Metaheuristic Computing, 2015
This paper introduces a local search optimization technique for solving efficiently a financial portfolio design problem which consists to affect assets to portfolios, allowing a compromise between maximizing gains and minimizing losses. This practical problem appears usually in financial engineering, such as in the design of CDO-squared portfolios. This problem has been modeled by Flener et al. who proposed an exact method to solve it. It can be formulated as a quadratic program on the 0-1 domain. It is well known that exact solving approaches on difficult and large instances of quadratic integer programs are known to be inefficient. That is why this work has adopted a local search method. It proposes neighborhood and evaluation functions specialized on this problem. To boost the local search process, it also proposes a greedy algorithm to start the search with an optimized initial configuration. Experimental results on non-trivial instances of the problem show the effectiveness of...
2014
In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The generalized model is formulated as a mixed integer quadratic programming (MIP) problem. The purpose of this paper is to investigate a continuous approach based on difference of convex functions (DC) programming for solving the MIP model. The preliminary comparative results of the proposed approach versus CPLEX are presented.
Expert Systems with Applications, 2009
Heuristic algorithms strengthen researchers to solve more complex and combinatorial problems in a reasonable time. Markowitz's Mean-Variance portfolio selection model is one of those aforesaid problems. Actually, Markowitz's model is a nonlinear (quadratic) programming problem which has been solved by a variety of heuristic and non-heuristic techniques. In this paper a portfolio selection model which is based on Markowitz's portfolio selection problem including three of the most important limitations is considered. The results can lead Markowitz's model to a more practical one. Minimum transaction lots, cardinality constraints (both of which have been presented before in other researches) and market (sector) capitalization (which is proposed in this research for the first time as a constraint for Markowitz model), are considered in extended model. No study has ever proposed and solved this expanded model. To solve this mixed-integer nonlinear programming (NP-Hard), a corresponding genetic algorithm (GA) is utilized. Computational study is performed in two main parts; first, verifying and validating proposed GA and second, studying the applicability of presented model using large scale problems.
Heuristic algorithms strengthen researchers to solve more complex and combinatorial problems in a reasonable time. Markowitz's Mean-Variance portfolio selection model is one of those aforesaid problems. Actually, Markowitz's model is a nonlinear (quadratic) programming problem which has been solved by a variety of heuristic and non-heuristic techniques. In this paper a portfolio selection model which is based on Markowitz's portfolio selection problem including three of the most important limitations is considered. The results can lead Markowitz's model to a more practical one. Minimum transaction lots, cardinality constraints (both of which have been presented before in other researches) and market (sector) capitalization (which is proposed in this research for the first time as a constraint for Markowitz model), are considered in extended model. No study has ever proposed and solved this expanded model. To solve this mixed-integer nonlinear programming (NP-Hard), a corresponding genetic algorithm (GA) is utilized. Computational study is performed in two main parts; first, verifying and validating proposed GA and second, studying the applicability of presented model using large scale problems.
A New Approach to Solve an Extended Portfolio Selection Problem
2012
In this paper, a Meta heuristic method is used to solve an extended Markowitz mean-variance portfolio selection model. Since the problem is modeled by quadratic integer programming, we should use Meta heuristics to solve it. This paper proposes a simulated annealing Meta heuristic method to solve the problem and the results for a large scale example is compared with genetic algorithm. The Computational results show that the proposed method is more efficient on large scale examples.
2012
Markowitz formulated the portfolio optimization problem through two criteria: the mean, representing the expected return, and the risk, a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. The LP solvability is very important for real-life decisions where the portfolios have to meet side constraints and take into account transaction costs. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of ...