Journal of Mathematics and Statistics

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

Anton Abdulbasah Kamil, Adli Mustafa and Khlipah Ibrahim

DOI : 10.3844/jmssp.2009.379.386

Journal of Mathematics and Statistics

Volume 5, Issue 4

Pages 379-386


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 &#34Here-and-Now&#34 approach where the decision-maker makes decision &#34now&#34 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.


© 2009 Anton Abdulbasah Kamil, Adli Mustafa and Khlipah Ibrahim. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.