Algorithmic Improvements of the KSU-STEM Method Verified on a Fund Portfolio Selection

The topic of this article is inspired by the problem faced by many people around the world: investment portfolio selection. Apart from the standardly used methods and approaches, non-traditional multiple objective programming methods can also be significant, providing even more efficient support for making a satisfactory investment decision. A more suitable method for this purpose seems to be a concept working with an interactive procedure through the portfolio that may gradually be adapted to the investor’s preferences. Such a method is clearly the Step Method (STEM) or the more suitable improved version KSU-STEM. This method is still burdened by partial algorithmic weaknesses or methodical aspects to think about, but not as much as the other methods. The potentially stronger application power of the KSU-STEM concept motivates its revision. Firstly, an unnecessarily negative principle to determine the basal value of the objectives is revised. Further, the fuzzy goals are specified, which leads to a reformulation of the revealed defuzzified multi-objective model. Finally, the imperfect re-setting of the weights (importance) of unsatisfactory objectives is revealed. Thus, the alternative approaches are proposed. The interventions to the algorithm are empirically verified through a real-life selection of a portfolio of the open unit trusts offered by CONSEQ Investment Management traded on the Czech capital market. This application confirms a significant supporting power of the revised multiple objective programming approach KSU-STEM in a portfolio-making process.

On compromise solutions in multiple objective programming

Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.