EXPLORING THE CONCEPT OF DERIVATIVE RISKS ARISING FROM EXTERNAL INFLUENCES IN THE CONTEXT OF BUSINESS OPERATIONS AND THEIR STRATEGIC STABILITY

In the modern operational environment, external factors play a decisive role in shaping the strategy and tactics of enterprise development. The dynamic changes in market, economic, political, social, and technological parameters necessitate the development of a systematic approach to analyzing the impact of external factors on internal business processes. One of the key aspects of such analysis is the assessment of derivative risk from influence development, which can be formalized as a functional dependence between external influences, business processes, and their outcomes. The objective of this study is to develop and substantiate a mathematical model for analyzing the development of external influences on the activities of business entities. This model aims to systematize the process of risk assessment and management through the use of quantitative analytical methods. The study formalizes the key components of the model, including the set of external influences, business processes, derivative risks, and the final state of the affected entity. The proposed model takes into account key external environmental factors – economic, political, social, environmental, and technological – and their impact on core business functions, such as operations, financial management, marketing, supply chain management, and human resources. Particular attention is paid to the mechanism of derivative risk formation, which is expressed through a system of equations that describe the dependencies between external influences and the dynamics of changes in business processes. Based on the mathematical framework, which includes linear and nonlinear dependencies, probabilistic analysis, and optimization methods, a system for quantitative and qualitative risk assessment has been developed. This approach enables effective risk forecasting and the formulation of optimal response strategies. The probabilistic approach facilitates the modeling of potential scenarios and the selection of the best decision-making options. The practical significance of the model lies in its application for strategic planning by identifying potential threats and opportunities, risk management based on quantitative analysis of their impact on business processes, resource optimization to minimize potential losses, enterprise adaptation to dynamic external changes, and enhancing operational efficiency through flexible business processes and proactive response strategies. Thus, the results of this study can be utilized as an effective tool for enhancing enterprise resilience, optimizing operations, and developing crisis management measures in response to external challenges.