Research Article Open Access

Stochastic Optimization for Portfolio Selection Problem with Mean Absolute Negative Deviation Measure

Anton Abdulbasah Kamil, Adli Mustafa and Khlipah Ibrahim

Abstract

Problem statement: The most important character within optimization problem is the uncertainty of the future returns. Approach: To handle such problems, we utilized probabilistic methods alongside with optimization techniques. We developed single stage and two stage stochastic programming with recourse. The models were developed for risk adverse investors and the objective of the stochastic programming models is to minimize the maximum downside semi deviation. We used the so-called "Here-and-Now" approach where the decision-maker makes decision "now" before observing the actual outcome for the stochastic parameter. Results: We compared the optimal portfolios between the single stage and two stage models with the incorporation of the deviation measure. The models were applied to the optimal selection of stocks listed in Bursa Malaysia and the return of the optimal portfolio was compared between the two stochastic models. Conclusion: The results showed that the two stage model outperforms the single stage model in the optimal and in-sample analysis.

Journal of Mathematics and Statistics
Volume 5 No. 4, 2009, 379-386

DOI: https://doi.org/10.3844/jmssp.2009.379.386

Submitted On: 9 October 2009 Published On: 31 December 2009

How to Cite: Kamil, A. A., Mustafa, A. & Ibrahim, K. (2009). Stochastic Optimization for Portfolio Selection Problem with Mean Absolute Negative Deviation Measure. Journal of Mathematics and Statistics, 5(4), 379-386. https://doi.org/10.3844/jmssp.2009.379.386

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Keywords

  • Portfolio optimization
  • maximum semi deviation measure
  • downside risk
  • stochastic linear programming