Portfolio optimization with an envelope-based multi-objective evolutionary algorithm
The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean-variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz' critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed. In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs.
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- Crama, Y. & Schyns, M., 2003. "Simulated annealing for complex portfolio selection problems," European Journal of Operational Research, Elsevier, vol. 150(3), pages 546-571, November.
- N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
- Schaerf, Andrea, 2002. "Local Search Techniques for Constrained Portfolio Selection Problems," Computational Economics, Springer;Society for Computational Economics, vol. 20(3), pages 177-190, December.
- Ehrgott, Matthias & Klamroth, Kathrin & Schwehm, Christian, 2004. "An MCDM approach to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 155(3), pages 752-770, June.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
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