Stochastic Modeling of Cyber Threat Risks in Smart Grids as a Tool of Economic Cybernetics

Abstract

The development of smart grids represents a fundamental direction in the digitalization of infrastructure within the knowledge economy. Smart grids enable efficient distribution of energy resources, integration of renewable sources, and real-time interaction between consumers and suppliers. However, the openness of their information and communication architecture significantly increases vulnerability to cyber threats. Attacks on power networks may cause not only technological disruptions but also large-scale economic losses, directly affecting the competitiveness of both states and enterprises. This paper emphasizes Smart Grid security as a critical factor of economic resilience. Economic cybernetics provides a methodological basis for assessing risks, while stochastic modeling offers quantitative tools for evaluating cyber threat probabilities and optimizing defense strategies. Methods such as Markov chains, Poisson processes, and stochastic Petri nets are applied to describe system state transitions, attack intensities, and interdependencies of infrastructure components. The main results of the study demonstrate that stochastic models allow the formalization of cyber threats in probabilistic terms, prediction of incident dynamics, calculation of resilience indicators, and justification of optimal investment levels in cyber defense. Furthermore, the integration of such results into economic management models enhances decision-making efficiency in balancing innovation, costs, and infrastructure stability. In conclusion, stochastic risk modeling contributes not only to the reliability and resilience of Smart Grids but also to the broader field of economic cybernetics, where mathematical methods support effective governance of socio-economic systems under conditions of cyber vulnerability. JEL: C02, C61, O33, Q43