The scenario modeling of regional competitiveness risks based on the Chapman-Kolmogorov equations

The paper is devoted to the development of analytical tools for assessing the dynamics of risks to the competitiveness of Russian regions within the conditions of incomplete information. The choice of analysis methods for assessing the risk dynamics was substantiated. A solution based on the implementation of homogeneous Markov models with a discrete set of states and continuous time was proposed, it allowed to assess the probability of risks affecting regional competitiveness. A hierarchical structure of factors that determine the risks of regional competitiveness was formed as a cause-and-effect graph. Corresponding systems of Kolmogorov – Chapman differential equations were obtained and solved. An example for analyzing a 3-element minimal cut set of a cause-effect graph was presented. A set of scenarios for the study of risks and their combinations in various conditions was proposed. The solution was obtained for three leading Russian regions. For a set of scenarios, numerical assessments of risk factors that significantly affect the decline in the competitiveness of regions have been fulfilled. The study results made it possible to rank the effects of critical event occurrence, to identify the most significant risk factors for the loss of sustainable development and competitiveness for the Russian Federation regions.