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Portfolio selection using neural networks. (English) Zbl 1102.91322

Summary: We apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the NN heuristic and we compare them to those obtained with three previous heuristic methods. The portfolio selection problem is an instance from the family of quadratic programming problems when the standard Markowitz mean-variance model is considered. But if this model is generalized to include cardinality and bounding constraints, then the portfolio selection problem becomes a mixed quadratic and integer programming problem. When considering the latter model, there is not any exact algorithm able to solve the portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search and simulated annealing have been developed. The purpose of this paper is to consider a particular neural network (NN) model, the Hopfield network, which has been used to solve some other optimization problems and apply it here to the portfolio selection problem, comparing the new results to those obtained with previous heuristic algorithms.

MSC:

91G10 Portfolio theory
90C59 Approximation methods and heuristics in mathematical programming
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References:

[1] Markowitz, H., Portfolio selection, Journal of Finance, 7, 77-91 (1952)
[2] Chang, T.-J.; Meade, N.; Beasley, J.; Sharaiha, Y., Heuristics for cardinality constrained portfolio optimisation, Computers & Operations Research, 27, 1271-1302 (2000) · Zbl 1032.91074
[3] Lin D, Wang S, Yan H. A multiobjective genetic algorithm for portfolio selection problem. In: Proceedings of ICOTA 2001. Hong Kong, 15-17 December 2001.; Lin D, Wang S, Yan H. A multiobjective genetic algorithm for portfolio selection problem. In: Proceedings of ICOTA 2001. Hong Kong, 15-17 December 2001.
[4] Streichert F, Ulmer H, Zell A. Evolutionary algorithms and the cardinality constrained portfolio optimization problem. In: Selected papers of the international conference on operations reasearch (OR 2003). Heidelberg, 3-5 September 2003.; Streichert F, Ulmer H, Zell A. Evolutionary algorithms and the cardinality constrained portfolio optimization problem. In: Selected papers of the international conference on operations reasearch (OR 2003). Heidelberg, 3-5 September 2003.
[5] Fieldsend J, Matatko J, Peng M. Cardinality constrained portfolio optimisation. In: Proceedings of the fifth international conference on intelligent data engineering and automated learning (IDEAL’04). Exeter, 25-27 August 2004.; Fieldsend J, Matatko J, Peng M. Cardinality constrained portfolio optimisation. In: Proceedings of the fifth international conference on intelligent data engineering and automated learning (IDEAL’04). Exeter, 25-27 August 2004.
[6] Xia, Y.; Liu, B.; Wang, S.; Lai, K., A model for portfolio selection with order of expected returns, Computers & Operations Research, 27, 409-422 (2000) · Zbl 1063.91519
[7] Schaerf, A., Local search techniques for constrained portfolio selection problems, Computational Economics, 20, 177-190 (2002) · Zbl 1036.91026
[8] Gilli M, Këllezi E. Heuristic approaches for portfolio optimization. In: Sixth international conference on computing in economics and finance of the society for computational economics. Barcelona, 6-8 July 2000.; Gilli M, Këllezi E. Heuristic approaches for portfolio optimization. In: Sixth international conference on computing in economics and finance of the society for computational economics. Barcelona, 6-8 July 2000.
[9] Kellerer H, Maringer D. Optimization of cardinality constrained portfolios with an hybrid local search algorithm. In: MIC’2001—4th Methaheuristics international conference. Porto, 16-20 July 2001.; Kellerer H, Maringer D. Optimization of cardinality constrained portfolios with an hybrid local search algorithm. In: MIC’2001—4th Methaheuristics international conference. Porto, 16-20 July 2001. · Zbl 1031.91054
[10] Sawaragi, Y.; Nakayama, H.; Tanino, T., Theory of multiobjective optimization, (Bellman, R., Mathematics in science and engineering, vol. 176 (1985), Academic Press Inc.: Academic Press Inc. New York) · Zbl 0435.90093
[11] Jobst, N.; Horniman, M.; Lucas, C.; Mitra, G., Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints, Quantitative Finance, 1, 1-13 (2001) · Zbl 1405.91559
[12] Smith, K., Neural networks for combinatorial optimization: a review of more than a decade of research, INFORMS Journal on Computing, 11, 1, 15-34 (1999) · Zbl 1034.90528
[13] Hopfield, J., Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences, 81, 3088-3092 (1984) · Zbl 1371.92015
[14] Peterson, C.; Söderberg, B., A new method for mapping optimization problems onto neural networks, International Journal of Neural Systems, 1, 3-22 (1989)
[15] Wang, X.; Jagota, A.; Botelho, F.; Garzon, M., Absence of cycles in symmetric neural networks, Neural Computation, 10, 5, 1235-1249 (1998)
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