The main objective of this article is to draw attention to the subject of portfolio management process, which is often not discussed in the professional literature. It has been shown that globalization affects the portfolio management process, which is presented in the literature in a similar manner. Thus, in this publication, the presentation of the process was made in terms of the classical one, and then the attempt was made to establish its form after the evolution that results from the above mentioned globalization. In addition, this new form is presented from the perspective of the use of artificial neural networks as organizations which invest cash primarily in financial instruments should take into account the mentioned expert tool for the purpose of further development. The publication also shows the key areas which the professional literature focuses on with regards to the subject of portfolio management. The study used the literature from the area of portfolio management, which is the basis for theoretical consideration, but these results have got the cognitive and practical value. They are a basis for separate quantitative research, and the proposed portfolio management process model can be considered cognitively interesting for researchers and investors.