Risk involves identifying several options that the decision-maker can opt for while making a choice either in the direction of risk or reliability. In this approach, risk is defined as the action of the subject which will lead to the loss or guaranteed safety of what has been achieved. As the uncertainty of the external business environment increases for companies, the task of managing risks both individually and as a set of risks becomes more and more relevant. The purpose of this study is to solve the problem of managing multifactorial risks using mathematical methods for determining the optimal risk management trajectories separately for each factor. To determine the optimal risk management trajectories for each factor, a numerical method is used based on the choice of the most effective direction, which is defined as the ratio of risk change to cost change. An information system prototype has been created that can support the management of a set of risks. Approbation of the information system was carried out on an example containing two conceptual risk factors. The proposed prototype builds a three-dimensional risk map by interpolating the risk matrix entered by the risk manager using an additive–multiplicative aggregation procedure, as well as optimal risk management trajectories for all entered risk factors.

The study identifies factors affecting the development of intellectual capital in companies. It is noted that there is a need to create a methodological framework for knowledge exchange and management. The results of the respondents’ surveys were analyzed, which made it possible to determine the priorities for the development of employees and organizations. The ways of achieving success by companies and the opinions of respondents responsible for understanding the term “knowledge” are revealed. The positive experience in connection with the exchange of information received is substantiated. The possibility of the influence of the accidental appearance of knowledge within companies is indicated.