New complex fuzzy multiple objective programming procedure for a portfolio making under uncertainty

Abstract

This article deals with a still current decision making problem — where to invest and how much. A few “tools” can help to answer this question, namely fundamental, technical or psychological analysis. “Soft” aspects as a human intuition or mood on the capital market can also play a nonnegligible role. These approaches and techniques (mainly individually) provide a partial information on investment reality. In practice, an investment decision, or portfolio, is mostly made just based on such a limited information. Moreover, the assets’ shares in the portfolio must be implicitly added up. This “crumbled” approach may not be an expected support to make a satisfactory investment decision. Therefore, a complex decision making procedure is practically designed. It is based on the fuzzy multiple objective programming method whose unique algorithm, working with triangular fuzzy numbers, is proposed in this article. Although these methods of decision making theory are not widely used on the capital market, they can be very convenient. The developed approach enables multiple objectives to be simultaneously accepted, as well as vague information about the assets or vague investor preferences. Moreover, a valuable output of this multi-factor procedure is an explicit quantification of the assets’ share in the portfolio. The ability to include all these aspects, which plays a significant role in a decision making on the capital market, proves a strong application power (and advantage over the mentioned concepts) to make an investment portfolio satisfactorily. This strength is demonstrated on the Czech capital market with open unit trusts offered by Česká spořitelna. Based on the specified investment strategy, the satisfactory investment portfolio consisting of four open unit trusts is effectively made.