Mathematical models of Ponzi schemes that consider the stochastic nature of decision-making

  • Grant A. Kesiyan Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia
  • Anna V. Kovalenko Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia
  • Makhamet Ali Kh. Urtenov Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia
  • Zulfa M. Laipanova Karachay-Cherkessian State University named after U. D. Aliev, 29 Lenina Street, Karachaevsk 369202, Russia
  • Anna V. Ovsyannikova Financial University under the Government of the Russian Federation, 49/2 Leningradskij Avenue, Moscow 125167, Russia

Abstract

In this paper, we further develop well-known approaches to modelling the functioning of Ponzi schemes and generalise them using stochastic differential equations in the Ito form. The applied models take into account the dependence of the scheme’s existence time on the accrued interest rate and the growth of the number of clients, as well as different variants of the advertising campaign. The obtained formulas and results of the corresponding experiments are given.

Author Biographies

Grant A. Kesiyan, Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia

senior lecturer at the department of data analysis and artificial intelligence, faculty of computer technology and applied mathematics

Anna V. Kovalenko, Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia

doctor of science (engineering), docent; head of the department of data analysis and artificial intelligence, faculty of computer technology and applied mathematics

Makhamet Ali Kh. Urtenov, Kuban State University, 149 Stavropolskaja Street, Krasnodar 350040, Russia

doctor of science (physics and mathematics), full professor; professor at the department of applied mathematics, faculty of computer technology and applied mathematics

Zulfa M. Laipanova, Karachay-Cherkessian State University named after U. D. Aliev, 29 Lenina Street, Karachaevsk 369202, Russia

PhD (physics and mathematics), docent; head of the department of mathematical analysis, faculty of physics and mathematics, and acting dean of the faculty of physics and mathematics

Anna V. Ovsyannikova, Financial University under the Government of the Russian Federation, 49/2 Leningradskij Avenue, Moscow 125167, Russia

PhD (pedagogics), docent; associate professor at the department of mathematics, faculty of information technology and big data analysis

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Published
2024-08-01
Keywords: mathematical modelling, financial pyramid, Ponzi scheme, stochastic differential equations, Ito processes, numerical Runge – Kutta scheme
How to Cite
Kesiyan, G. A., Kovalenko, A. V., Urtenov, M. A. K., Laipanova, Z. M., & Ovsyannikova, A. V. (2024). Mathematical models of Ponzi schemes that consider the stochastic nature of decision-making. Journal of the Belarusian State University. Mathematics and Informatics, 2, 27-39. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/6358
Issue
No 2 (2024): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

Copyright (c) 2024 Journal of the Belarusian State University. Mathematics and Informatics

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