Portfolio Optimization With Buy-in Thresholds Constraint Using Simulated Annealing Algorithm

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Indana Lazulfa Pujo Hari Saputro


Portfolio optimization is a solution for investors to get the return as much as possible and also to minimize risk as small as possible. In this research, we use risk measures for portfolio optimization, namely mean-variance model. For single objective portfolio optimization problem, especially minimizing risk of portfolio, we used mean-variance as risk measure with constraint such as buy-in thresholds. Buy-in thresholds set a lower limit on all assets that are part of portfolio. All this portfolio optimization problems will be solved by simulated annealing algorithm. The performance of the tested metaheuristics was good enough to solve portfolio optimization.

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LAZULFA, Indana; SAPUTRO, Pujo Hari. Portfolio Optimization With Buy-in Thresholds Constraint Using Simulated Annealing Algorithm. Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami), [S.l.], v. 1, n. 1, p. 370-377, july 2017. Available at: <http://conferences.uin-malang.ac.id/index.php/SIMANIS/article/view/132>. Date accessed: 25 apr. 2024.


[1] Crama, Y., Schyns, M. 2001. Simulated Annealing for Complex Portfolio Selection Problems. University of University of Liége, Bd. Du Rectorat 7, Liége, Belgium.
[2] Bonami, P., Lejeune, M.A. 2009. An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints. Journal Operation Research, 57, 650-670.
[3] Ingber, L. 1993. Simulated Annealing : Practice Versus Theory. Mathematical Computation Modelling 18. 11. 29-57.
[4] Biggs, M.B. & Kane, S.J. 2007. A Global Optimization in Portfolio Selection. Journal Management Science, 6, 329–345.
[5] Jobst, N.J., Horniman, M.D., Lucas, C.A. & Mitra, G. 2001. Computational Aspects of Alternative Portfolio Selection Models in The Presence of Discrete Asset Choice Constraints. Quantitative Finance. Vol 1. 1–13.
[6] Chang, T.J., Yang, S.C. & Chang, K.J. 2009. Portfolio Optimization Problems in Different Risk Measures Using Genetic Algorithm. Expert System with Application, 36, 10529–10537.
[7] Markowitz, H.M. 1952. Portfolio Selection. Journal of Finance 7. pp 77–91.
[8] Elton, E.J. Gruber, M.J. 1991. Modern Portfolio Theory and Investment Analysis 4th edition. John Wiley : New York – London.
[9] Bartholomew-Biggs, M. 2005. Nonlinear Optimization with Financial Applications. Kluwer Academic Publisher.
[10] Hull, J.C. 2012. Options, Futures, and Other Derivatives Eighth Edition. Pearson, Prentice Hall : United States of America.
[11] Van Laarhoven P.J.M., Aarts E.H.. 1988. Simulated Annealing : Theory and Applications. Kluwer Academic Publishers.
[12] Aarts, E., Lenstra, J.K.. 1997. Local Search in Combinatorial Optimization. John Wiley & Sons : New York.
[13] Pirlot M. 1992. General Local Search Heuristics in Combinatorial Optimization : A Tutorial. Belgian Journal of Operations Research, Statistics and Computer Science 32. Pp 7–68.
[14] Kirkpatrick, S., Gelatt, C.D., Vecchi, P.M. 1983. Optimization by Simulated Annealing. Science 220. Pp 671–680.