Abstract
A portfolio optimization problem involves optimal allocation of finite capital to a series of assets to achieve an acceptable trade-off between profit and risk in a given investment period. In the paper, the extended Markowitz’s mean-variance portfolio optimization model is studied. A major challenge with this model is that it contains both discrete and continuous decision variables, which represent the assignment and allocation of assets respectively. To deal with this hard problem, this paper proposes an evolutionary algorithm with a new coding scheme that converts discrete variables into continuous ones. By this way, the mixed variables can be handled, and some of the constraints are naturally satisfied. The new approach is empirically studied and the experiment results indicate its efficiency.
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References
Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6(2), 154–160 (1994)
Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74(2), 121–140 (1996)
Chang, T.-J., Meade, N., Beasley, J.E., Sharaiha, Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27(13), 1271–1302 (2000)
Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11), 1245–1287 (2002)
Elton, E.J., Gruber, M.J.: Investments and Portfolio Performance. World Scientific, Singapore (2011)
Grinblatt, M., Titman, S., Wermers, R.: Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior. Am. Econ. Rev. 1088–1105 (1995)
Gulpinar, N., An, L.T.H., Moeini, M.: Robust investment strategies with discrete asset choice constraints using DC programming. Optimization 59(1), 45–62 (2010)
Lwin, K., Rong, Q., Kendall, G.: A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Appl. Soft Comput. 24, 757–772 (2014)
Mansini, R., Speranza, M.G.: Heuristic algorithms for the portfolio selection problem with minimum transaction lots. Eur. J. Oper. Res. 114(2), 219–233 (1999)
Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)
Newman, A.M., Weiss, M.: A survey of linear and mixed-integer optimization tutorials. INFORMS Trans. Educ. 14(1), 26–38 (2013)
Robič, T., Filipič, B.: DEMO: differential evolution for multiobjective optimization. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31880-4_36
Shaw, D.X., Liu, S., Kopman, L.: Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optim. Methods Softw. 23(3), 411–420 (2008)
Sierra, M.R., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and \(\epsilon \)-dominance. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31880-4_35
Skolpadungket, P., Dahal, K., Harnpornchai, N.: Portfolio optimization using multi-objective genetic algorithms. In: 2007 IEEE Congress on Evolutionary Computation, pp. 516–523. IEEE (2007)
Steuer, R.E., Hirschberger, M., Deb, K.: Extracting from the relaxed for large-scale semi-continuous variable nondominated frontiers. J. Glob. Optim. 64(1), 33–48 (2016)
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Streichert, F., Ulmer, H., Zell, A.: Evolutionary algorithms and the cardinality constrained portfolio optimization problem. In: Ahr, D., Fahrion, R., Oswald, M., Reinelt, G. (eds.) ORP 2003. Operations Research Proceedings, vol. 2003, pp. 253–260. Springer, Heidelberg (2004). doi:10.1007/978-3-642-17022-5_33
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Acknowledgement
This work is supported by the Shanghai Clearing House under the project of ‘artificial intelligence methods for complex 0-1 financial optimization’, the National Natural Science Foundation of China under Grant No. 61673180, and the Science and Technology Commission of Shanghai Municipality under Grant No. 14DZ2260800.
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Chen, Y., Zhou, A., Zhou, R., He, P., Zhao, Y., Dong, L. (2017). An Evolutionary Algorithm with a New Coding Scheme for Multi-objective Portfolio Optimization. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_9
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