Title: A study on discrete Ponzi Scheme model through Sturm-Liouville theory

Authors: Ferhan Merdivenci Atıcı; William R. Bennett

Addresses: Department of Mathematics, Western Kentucky University, Bowling Green, KY, 42101-3576, USA ' Department of Economics, Western Kentucky University, Bowling Green, KY, 42101, USA

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.

Keywords: Ponzi scheme; difference equation; Sturm-Liouville boundary value problem; Green's function; discrete calculus; Charles Ponzi; investment; rate of return.

DOI: 10.1504/IJDSDE.2021.117359

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.227 - 240

Received: 20 Apr 2020
Accepted: 29 Sep 2020
Published online: 01 Sep 2021 *

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