Slyuz A. Mathematical modeling of risk assessment in enterprise management

The dissertation develops theoretical, methodological and applied foundations for enterprise risk assessment based on economic and mathematical modeling. The study proposes a comprehensive toolkit for assessing production risks under conditions of uncertainty and supporting effective managerial decision-making. The relevance of the research is determined by the growing uncertainty of the Ukrainian economy caused by prolonged military aggression, which has significantly increased risks for business activity. Enterprises operate in an unstable environment characterized by resource constraints, market volatility and changing consumer demand. Under such conditions, effective risk assessment and management become essential prerequisites for maintaining competitiveness and ensuring sustainable development. Modern enterprise management therefore requires scientifically grounded methods capable of identifying, assessing and minimizing the impact of risks. The aim of the dissertation is to develop an economic and mathematical toolkit for modeling and assessing production risks while accounting for uncertainty in the internal and external environment of enterprises. The object of the research is the economic processes of managing enterprise production activities under risk. The subject of the research is the methodology and economic and mathematical models for assessing risks and improving the efficiency of enterprise management. The dissertation consists of an introduction, three chapters, conclusions, references and appendices. The first chapter investigates entrepreneurship as a fundamental component of the national economy and analyzes the influence of innovation, competition and uncertainty on enterprise development. The economic nature of entrepreneurial risk is examined, and a classification of business risks is proposed according to their causes, characteristics and consequences. Risk is considered as a multidimensional category that combines threats, opportunities and uncertainty. The necessity of applying quantitative methods for forecasting and risk assessment in enterprise management is substantiated. The second chapter analyzes the current state of entrepreneurial activity in Ukraine and identifies the key factors affecting business sustainability under wartime conditions. A combined methodology integrating qualitative and quantitative approaches to risk assessment is justified, allowing expert judgment to complement formal analytical methods. An economic and mathematical production optimization model is developed that considers uncertainty in resource availability and market conditions, enabling enterprises to adapt production strategies and reduce potential losses. The third chapter presents an economic and mathematical optimization model based on the Monte Carlo simulation method. The model incorporates stochastic demand, fluctuations in resource availability and changes in prices, providing an opportunity to evaluate alternative production strategies under uncertainty. Scenario analysis demonstrates the influence of demand volatility and resource constraints on enterprise performance. The results show that shortages of production resources significantly reduce expected profits and increase the level of risk, whereas accounting for heterogeneous demand volatility improves the stability of production outcomes. Bakery products and cookies proved to be more resistant to adverse changes than confectionery products, which are more sensitive to increases in raw material costs and resource shortages. Quantitative risk assessment was performed using the Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) indicators. An optimization model focused on maximizing consolidated cash flow was also developed. The model integrates production and financial decision-making while incorporating risk adjustments, making it possible to identify optimal production programs and financing strategies that enhance enterprise financial stability. The dissertation proposes practical recommendations for improving the sustainability of food industry enterprises through efficient resource allocation, adaptation of production processes to changing market conditions, substitution of resource-intensive products and integration of operational and financial planning within a unified optimization framework. The practical significance of the research lies in the possibility of applying the proposed models and methods to improve enterprise risk management, optimize production strategies, increase financial stability and reduce potential losses. The developed approaches may be used in strategic planning, anti-crisis management, financial forecasting and higher education courses in economic and mathematical modeling, operations research and risk management.