5.4.2 Methods of Stochastic Analysis in the Study of Human Behavior in the Context of Global Challenges

Research Area 5.. Neurocognitive Mechanisms of Social Behavior → Research Program 5.4 Neurocognitive Decision-making Mechanisms in Different Social Contexts

Project period

2024-2025

Context of Research Project within a Subject of Human Capital

The development of human potential takes place in the constant overcoming of mutual challenges. Among them are the challenges to the environment caused by the human side and the challenges to human caused by the environment around him. Since this interaction contains many factors that cannot be clearly described, researchers turn to the elements of stochastic (probabilistic) analysis.

The research project Methods of Stochastic Analysis in the Study of Human Behavior in the Context of Global Challenges focuses on three areas of use of stochastic analysis models in the study of factors affecting the development of human potential. Among them are the study of the objectives of social interaction with a large number of participants under the assumption of individual rationality and uniformity, the study of mathematical methods of models of optimal forest care in order to preserve it from fires, harmful insects and plants, and the study of human potential development associated with the expansion of knowledge about the dynamics of key economic indicators.

Project Aim

Constructing probabilistic models (models of social interaction with a large number of participants, models of stochastic optimal control, models of jump processes) capable of realistically describing the processes occurring in the era of technological transformations, and the study of the characteristics of these models by stochastic analysis methods.

Project objectives:

1. Describing maximum values of stock price based on a model of a mixture of distributions with non-standard components, develop mathematical models for describing the dynamics and predicting extreme values of financial time series
2. Analyzing the correlation between practical problems of resource management, sustainability and optimality of their consumption, and mathematical problems about the existence and construction of solutions to the corresponding differential equations (systems of direct equations of the McKean-Vlasov type and inverse equations of the Hamilton-Jacobi-Bellman type)
3. Researching the model of the spread of infectious diseases, taking into account individual rationality within the framework of models of the mean field games with a finite number of states
4. Constructing mathematical models of optimal forest care and models of corruption schemes for illegal destruction, logging, removal of forests, protection from harmful insects (ticks), as well as environmental pollution by industrial waste

Key Findings

2024

The scientific project has been implemented since 2024