MATHEMATICAL MODELING OF RISKS IN PROJECT MANAGEMENT

ABSTRACT

The article discusses the problem of increasing the effectiveness of risk management in projects in conditions of high uncertainty and a constantly changing external environment. The subject of the research is modern methods of mathematical modeling. The object of research is risk management processes in various fields. The study used methods of system analysis, comparative evaluation and practical modeling. Aspects such as forecasting accuracy, adaptability of methods and their applicability in Russian realities are considered. The author's contribution to the research is the systematization of modern methods and their practical applications, as well as the identification of the main trends in the development of risk management. The author concludes that successful risk management requires the collaboration of several areas.

Keywords: risk management, methods, analysis, decision trees, artificial intelligence, machine learning, project, modeling.

With the development of technology in the world, modern projects face a high degree of uncertainty due to constantly changing environmental conditions, economic instability, technological changes, as well as the globalization of the economy. This is especially true in areas such as IT, construction, energy, and finance. Risk management becomes essential for the successful implementation of projects, otherwise unaccounted-for threats can lead to serious financial losses, exceeding deadlines, and even complete failure of the project. Traditional risk assessment methods often turn out to be subjective and insufficiently accurate. In turn, mathematical models make it possible to identify dependencies and predict the consequences most accurately.

The most common method of assessing project risks is the Monte Carlo method, a statistical simulation method that allows estimating uncertainty and risks by generating a set of random event outcomes based on probability distributions. In project management, it can be used to: predict the timing and cost of a project, taking into account uncertainty, calculate the probability of occurrence of risk events, and determine the "reserve" budget and time. According to this method, input parameters (duration of tasks, cost of resources) are first set with their probabilistic distributions, then a multiple (thousands or millions of times) simulation of the project is carried out taking into account random variations, and after all the work done, a probabilistic model of possible outcomes is built based on the results obtained. For example, if a project has a task with an optimistic estimate of 10 days, a pessimistic estimate of 20 days, and the most likely estimate of 15 days, the Monte Carlo method will show how these variations will affect the completion date.

In addition to the Monte Carlo method, decision trees are used in project risk assessment. This is a graphical method of risk analysis that allows you to structure possible solutions, their consequences and the likelihood of events. The method provides a structured representation of complex solutions, a visual visualization of alternatives and their consequences, the ability to evaluate various scenarios, and, in addition, the integration of probabilistic and cost analysis. The decision tree has its own structural elements: decision nodes (indicated by squares) are the points of choice between alternative strategies; probability nodes (indicated by circles) are the points of occurrence of uncontrolled events; branches are possible ways of developing the situation; end nodes are the final results indicating their value. For this method, the calculation of the expected monetary value for each branch is used according to a certain formula, which is the final sum of the products of the probability of the ith outcome and its cost estimate.

Another equally important method of assessing project risks is AI analysis. Modern artificial intelligence technologies are changing and developing approaches to project management. AI analysis allows you to automate the process of identifying risks, predict potential threats with high accuracy, improve risk response strategies, and process large amounts of data.

The main AI technologies for risk analysis are divided: machine learning - supervised learning to predict known risks and uncontrolled learning to identify new, previously unknown threats; deep learning – neural network models for processing complex unstructured databases (for example, text reports, news feeds); natural language processing – automatic analysis of project documents, identification of "risk signals" in participants' correspondence; cognitive technologies – decision support systems based on past cases.

In Russia, AI analysis is used in practice in construction megaprojects (according to Rosstat, 2023) and IT development (Skolkovo study, 2022).

AI analysis is revolutionizing traditional risk management. Russian companies are actively implementing these technologies, but some improvements are required to fully unlock their potential.

The most effective results are achieved by combining the methods listed above. Modern approaches to mathematical modeling of risks in project management have practical significance for Russian realities, as well as development prospects. Research shows that the introduction of mathematical modeling methods can reduce financial losses by 15-25%, reduce the number of deadlines by 30-40% and increase the accuracy of forecasts by 2-3 times. Modern project risk management requires a fusion of mathematical rigor, technological capabilities, and managerial evaluation.

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