brand portfolio; fractal environment; long-range system; fractional differential equation; fractional entropy


In the past twenty years or so, three approaches to brand portfolio management strategies have emerged. The first approach is marketing. This approach is associated with building a corporate brand portfolio. The goal is to increase diversified cash flows by entering new market segments. The second approach is related to the competitive strategy of the enterprise. A false portfolio of intellectual property applications is being created. Competitors are expected to spend resources in retaliation. The third approach is the formation of a dynamic strategy for investment portfolio management. Due to the complex structure of the modern global financial market, the heterogeneous structure of available financial instruments and traders using different approaches and time horizons, forecasts, as a rule, require a large number of observations, work poorly in the vicinity of bifurcations and do not have a computer model that could build forecasts in real time. In such structures, slow diffusion-type processes with the phenomenon of memory arise, that is, non-Markov processes. Moreover, such structures can have fractal properties. In this work, it seems to us, the first step has been taken to build a "synthetic" model of dynamic asset portfolio management. By analyzing the data available in the scientific literature, a mathematical model of strategic brand portfolio management is proposed. In view of the above, the model has the form of a differential equation in fractional derivatives. In connection with the risk analysis, two models of fractional entropy are also considered - fractional Kolmogorov-Sinai entropy and fractional Shannon entropy.

Author Biographies

Olena Akhiiezer, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences, Professor

Yevgen Gomozov, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Physical and Mathematical Sciences, Associate Professor

Anton Rogovyi, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences, Associate Professor


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