Stochastic modeling in risk analysis: methodological framework and comparative assessment

Abstract

In the context of global digitalization of socio-economic processes, the development of effective approaches to organizational risk management is becoming particularly urgent. This is driven by the need for flexible and ac-curate analytical tools capable of accounting for multiple risk factors and large data volumes, as well as for assessing risks in real time before they impact the socio-economic system. This paper provides a comparative analysis of three key statistical methods for risk assessment: Markov chains, Bayesian analysis, and the Monte Carlo method. Using a case study on borrower credit risk assessment, the capabilities and limitations of each technique are demonstrated. The study substantiates the expediency of applying Markov chains to model credit portfolio dynamics and borrower migration between rating categories. The Bayesian analysis is used for the sequential risk assessment of individual borrowers based on incoming discrete data. The Monte Carlo method is used to obtain a complete probability distribution of financial outcomes, accounting for the uncertainty of key economic variables. The study concludes that these methods are not interchangeable and that their integrated application enhances the robustness of risk assessment results.