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

Research Area 1. Social Science and Humanities Aspects of Human Capital → Research Program 1.1 Social Structure and Wellbeing of Households in the Framework of Sustainable Development Indicators

Project period

2020-2023

Since 2024, the project has been implemented as part of the Research Program 5.4 Neurocognitive Decision – making Mechanisms in Different Social Contexts

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

2020

The scientific project has been implemented since 2021

2021

A new mathematical result has been obtained, which can be called the quadratic penalty principle, showing that an effective fight against corruption is possible with the introduction of a penalty that depends quadratically on illegal income. The prospects of using a mixture of distributions for modeling stock prices in comparison with classical approaches have been studied.

2022

New diffusion models of tick settlement have been developed with an emphasis on heterogeneity of the habitat. The simulation of the size of control zones with artificially created unfavorable conditions, the presence of which leads to the extinction of ticks throughout the territory where such zones are created, has been carried out.

The graphics of the model of the decreasing number of ticks in the territory containing 3 control zones according to the predictions of the theory. The x coordinate characterizes the distance (in km), the t coordinate is time, the vertical density of the tick population is postponed as a function of space and time

2023

To solve the problem of finding the optimal frequency of barriers to the spread of ticks (bands unfavorable for their survival), a diffusion model of the spread of ticks was constructed, considering the heterogeneity of the settlement area and the structure of generations (larvae/nymphs and adult ticks, which differ greatly in the spread of spatial movements).

Based on the available data from field studies of the behavior of ticks (carried out by both researchers in North America and Russian scientists in Siberia), an estimate of the distance between barriers was obtained, which makes it possible to effectively prevent their spread. This mark was 45 km.

Publications

1. Kolokoltsev V. Inspection -corruption game of illegal logging and other violations: generalized evolutionary approach // Mathematics MDPI, 9(14), 1619
2. Panov V., Morozova E. Extreme value analysis for mixture models with heavy-tailed impurity // Mathematics MDPI, 9(18), 2208
3. Averboukh Y. Control theory approach to continuous-time finite state mean field games //arXiv preprint arXiv:2103.07493. – 2021. doi
4. Kolokoltsov V. N. (2022) On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model //Mathematics. – 2023. – Т. 11. – №. 2. – P. 478. doi
5. Yurii Averboukh. (2023) Control theory approach to continuous-time finite state mean field games //Mathematical Control and Related Fields. – 2023. – Т. 13. – №3. – Р. 1109-1130. doi
6. Kolokoltsov V. N., Vetchinnikov D. V. (2023) On Effective Fine Functions for Inspection—Corruption Games (Evolutionary Approach) //Mathematics. – 2023. – Т. 11. – №. 15. – P. 3429. doi
7. Averboukh Y., Volkov A. (2023) Planning problem for continuous-time finite state mean field game with compact action space //Dynamic Games and Applications. – 2023. – P. 1-19. doi

Conferences

10^th Bernoulli-IMS World Congress in Probability and Statistics (Seoul, Korea, July 19-23, 2021): Morozova E. Extreme Value Analysis аor Mixture Models With Heavy-Tailed Impurity [Contributed talk]

12^th International Conference on Extreme Value Analysis (EVA2021) (Edinburgh, Scotland, June 28 – July 2, 2021): Morozova E. Extreme Value Analysis for Mixture Models With Heavy-Tailed Impurity [Contributed talk]

XII International Academic Conference for undergraduate, graduate and PhD students on Statistical Methods Application for Analysis of Economics and Society (Moscow, Russia, May 11-14, 2021): Morozova E. Extreme Value Analysis for Mixture Models With Heavy-Tailed Impurity

International Conference Optimal Control and Fractional Dynamics, (Cambridge, UK, April 19-22, 2022): Kolokoltsev V. Fractional Forward-Backward Systems of Banach-Space Valued HJB and Mckean-Vlasov Equations Arising in Fractional Mean-Field Games

International Conference Modern Trends in Controlled Stochastic Processes (Liverpool, July 5-9, 2021): Kolokoltsev V. Games of Inspection and Corruption: Generalized Evolutionary Approach

Online scientific conference LSA Autumn Colloquium 2021 (Moscow, Russia, September 20-24, 2021): Kolokoltsev V. Against Ticks with Functional Analytic Guns