Geodesic
Mathematical models of ponzi schemes that consider the stochastic nature of decision-making
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2024), pp. 27-39.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: mathematical modelling; financial pyramid; Ponzi scheme; stochastic differential equations; Ito processes; numerical Runge – Kutta scheme 
@article{BGUMI_2024_2_a2,
     author = {A. V. Kovalenko and M. H. Urtenov and A. V. Ovsyannikova and G. A. Kesiyan and Z. M. Laipanova},
     title = {Mathematical models of ponzi schemes that consider the stochastic nature of decision-making},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {27--39},
     publisher = {mathdoc},
     volume = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a2/}
}
TY  - JOUR
AU  - A. V. Kovalenko
AU  - M. H. Urtenov
AU  - A. V. Ovsyannikova
AU  - G. A. Kesiyan
AU  - Z. M. Laipanova
TI  - Mathematical models of ponzi schemes that consider the stochastic nature of decision-making
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2024
SP  - 27
EP  - 39
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a2/
LA  - ru
ID  - BGUMI_2024_2_a2
ER  - 
%0 Journal Article
%A A. V. Kovalenko
%A M. H. Urtenov
%A A. V. Ovsyannikova
%A G. A. Kesiyan
%A Z. M. Laipanova
%T Mathematical models of ponzi schemes that consider the stochastic nature of decision-making
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2024
%P 27-39
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a2/
%G ru
%F BGUMI_2024_2_a2
A. V. Kovalenko; M. H. Urtenov; A. V. Ovsyannikova; G. A. Kesiyan; Z. M. Laipanova. Mathematical models of ponzi schemes that consider the stochastic nature of decision-making. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2024), pp. 27-39. http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a2/

[1] A. V. Kovalenko, M. Kh. Urtenov, R. Kh. Chagarov, “Matematicheskoe modelirovanie deyatelnosti finansovoi piramidoi. Chast 1, Osnovnye ponyatiya”, Politematicheskii setevoi elektronnyi nauchnyi zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta [Elektronnyi resurs], 2012, 8

[2] A. V. Kovalenko, M. Kh. Urtenov, R. Kh. Chagarov, “Matematicheskoe modelirovanie deyatelnosti finansovoi piramidoi. Chast 2, Osnovnye ponyatiya”, Politematicheskii setevoi elektronnyi nauchnyi zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta [Elektronnyi resurs], 2012, 8

[3] A. V. Kovalenko, M. Kh. Urtenov, R. Kh. Chagarov, “Matematicheskoe modelirovanie deyatelnosti finansovoi piramidoi. Chast 3, Osnovnye ponyatiya”, Politematicheskii setevoi elektronnyi nauchnyi zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta [Elektronnyi resurs], 2012, 8

[4] S. V. Dubovskii, Prognozirovanie inflyatsii i obmennogo kursa rublya v rossiiskoi nestatsionarnoi ekonomike, URSS, Moskva, 2001, +40 pp.

[5] S. V. Dubovskii, “Obmennyi kurs rublya kak rezultat denezhnoi emissii, vneshnei torgovli i bluzhdayuschikh finansovykh potokov”, Ekonomika i matematicheskie metody, 38(2) (2002), 84–96

[6] M. Artzrouni, “The mathematics of Ponzi schemes”, Mathematical Social Sciences, 58(2) (2009), 190–201 | DOI

[7] P. D. Huynh, S. H. Dau, X. Li, P. Luong, E. Viterbo, “Improving robustness and accuracy of Ponzi scheme detection on Ethereum using time-dependent features”, arXiv, 2023, 17 | DOI

[8] S. Fan, S. Fu, H. Xu, X. Cheng, “Al-SPSD: anti-leakage smart Ponzi schemes detection in blockchain”, Information Processing and Management, 58(4) (2021), 102587 | DOI

[9] d. e. van, S. Coneys, Classifying bitcoin Ponzi schemes with machine learning [Internet], New York University Shanghai, Shanghai, 2018, +8 pp. | DOI

[10] J. L. Gastwirth, “A probability model of a pyramid scheme”, The American Statistician, 31(2) (977), 79–82 | DOI

[11] A. Belianin, O. Issoupova, Financial pyramids in transitional economies: a game-theoretic approach, EERC, Moscow, 2001, +70 pp.

[12] A. K. Novikov, A. A. Osadchii, Matematicheskoe modelirovanie protsessov pritoka i ottoka kapitala v strukture finansovoi piramidy i realizatsiya modeli na EVM [Internet], Moskovskii gosudarstvennyi universitet imeni MV Lomonosova, Moskva, 2022, +41 pp.

[13] G. A. Kesiyan, M. Kh. Urtenov, A. V. Kovalenko, Matematicheskie modeli tsenoobrazovaniya na rossiiskom rynke tsennykh bumag, Kubanskii gosudarstvennyi universitet, Krasnodar, 2014, +158 pp.