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MODELLING PONZI SCHEMES AS A DIFFUSIVE PROCESS: A NOVEL PDE FRAMEWORK AND ANALYSIS | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مهر 1405 اصل مقاله (1.74 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70402.3497 | ||
| نویسنده | ||
| Emmanuel Obaro Ohwadua* | ||
| Department of Mathematical Sciences, Faculty of Science and Tehchology, Bingham University, Karu, Nigeria. | ||
| چکیده | ||
| The paper discusses the development of a novel Partial Differential Equation (PDE) framework to model and analyse the dynamics of Ponzi schemes, focusing on investor capital distribution and sustainability conditions. While PDEs have been a foundation to modern quantitative finance, their application in the context of the specific problem of Ponzi schemes have been limited. The existing literature is deficient in spatio-temporal (partial derivatives of cashflows and time), distribution-based model that can describe the continuous evolution of the investor capital distribution over time. It also does not incorporate advection (the aging of investments), diffusion (the spread of investment sizes), and source/sink terms (new investments/withdrawals) in a single cohesive framework. Our proposed PDE-based model is designed to describe the bubble and bust cycle of the schemes through the extension of the aggregate view of most differential equation-based models to a continuous setting and provides the analytical tractability that is often missing in complex ABMs (agent-based models). By drawing on the mathematical traditions of other PDE-based models, we offer a novel and rigorous tool for understanding the life cycle of this type of financial fraud – Ponzi scheme. | ||
| کلیدواژهها | ||
| Financial investment؛ financial fraud؛ cashflow؛ recruitment rate؛ withdrawal rate | ||
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