Introduction. To assess the investment attractiveness (IA) and development opportunities for investment objects (IO), non-financial factors characterizing the environmental, social, governance and technogenic (ESGT) features of objects of possible financing have been increasingly used recently. The purpose of this data analysis is to establish how the ESGT-parameters of IO may reflect their financial health and performance prospects in a rapidly changing world. Having built an ESGT risk profile with the help of mathematical models, the IA of the object of study and the strategy of practical measures to increase it are determined. When modeling these processes, one should consider the growing uncertainty of the modern world due to the emergence of new risks; a large number of systemic links between the structures of the modern technosphere; the power-law nature of the distribution of the probability density of catastrophe damage, which decreases more slowly than the Gaussian dependence. In addition, the efficiency of complex production systems is largely determined by the balance of their individual links. Therefore, to assess investment risks, new methods are required to formalize the dependence of IA on ESGT-factors for the integrated management of the level of credit, market, insurance and operational risks under conditions of uncertainty.
The purpose of the article is to develop mathematical methods for quantifying IA and determining real costs to improve the management, social and technological structure of IO, and minimize environmental pollution.
Results. A mathematical model has been developed for assessing the environmental, social, managerial and technogenic leaving risks of investment, which makes it possible to determine the optimal strategies for increasing the IA of a possible IO. For a comprehensive risk assessment, methods of the theory of singularities of smooth reflections (TOGO) and the method of analysis of hierarchies (MAH) are used. The following algorithm for estimating IA is proposed: 1) determining the indices of the ESGT-components of risk; 2) calculation of bifurcation index values; 3) determination of the weakest links, which are associated with a decrease in IA; 4) identification of priority measures to prevent the reduction of IA or restore it to a predetermined level and minimize the negative impacts of extreme events and ensure sustainable development.
Conclusions. The obtained results show that mathematical models based on the use of TOGO and MAH methods are an important tool for estimating IA under conditions of uncertainty. They allow: 1) to calculate the degree of approximation of the parameters characterizing the functioning of the object to their critical values ??when the IA changes; 2) to determine effective controls to minimize the risk of losing IA or minimize the time and losses for returning IA; 3) to consider the uncertainty factor associated with the features of the decision-making process. The development of this work is aimed at creating an information system for assessing IA for the integrated management of the level of credit, market, insurance and operational risks in the face of uncertainty and determining effective scenarios for minimizing investment risks. Keywords: mathematical modeling, system analysis, investment risks.