A study on discrete Ponzi Scheme model through Sturm-Liouville theory
by Ferhan Merdivenci Atıcı; William R. Bennett
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 11, No. 3/4, 2021

Abstract: In this paper, we introduce a second order self-adjoint difference equation which describes the dynamics of Ponzi schemes: a type of investment fraud that promises more than it can deliver. We use the Sturm-Liouville theory to study the discrete equation with boundary conditions. The model is based on a promised, unrealistic interest rate r_p, a realised nominal interest rate r_n, a growth rate of the deposits r_i, and a withdrawal rate r_w. Giving some restrictions on the rates r_p, r_i, and r_w, we prove some theorems to when the fund will collapse or be solvent. Two examples are given to illustrate the applicability of the main results.

Online publication date: Wed, 01-Sep-2021

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