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The mathematics of Ponzi schemes

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  • Artzrouni, Marc

Abstract

A first order linear differential equation is used to describe the dynamics of an investment fund that promises more than it can deliver, also known as a Ponzi scheme. The model is based on a promised, unrealistic interest rate; on the actual, realized nominal interest rate; on the rate at which new deposits are accumulated and on the withdrawal rate. Conditions on these parameters are given for the fund to be solvent or to collapse. The model is fitted to data available on Charles Ponzi's 1920 eponymous scheme and illustrated with a philanthropic version of the scheme.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14420.

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Date of creation: 02 Apr 2009
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Handle: RePEc:pra:mprapa:14420

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Keywords: Ponzi scheme; differential equation; market; bond;

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  1. Olivier J. Blanchard & Philippe Weil, 2001. "Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty," Sciences Po publications info:hdl:2441/8607, Sciences Po.
  2. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, Elsevier, vol. 12(1), pages 2-24, January.
  3. Stephen A. O'Connell & Stephen P. Zeldes, . "Rational Ponzi Games," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 18-86, Wharton School Rodney L. White Center for Financial Research.
  4. Forslid, Rikard, 1998. "External Debt and Ponzi-Games in a Small Open Economy with Endogenous Growth," Journal of Macroeconomics, Elsevier, Elsevier, vol. 20(2), pages 341-349, April.
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Cited by:
  1. Parodi, Bernhard R., 2013. "Abc-Modell eines Ponzi-Systems
    [Abc-model of a Ponzi system]
    ," MPRA Paper 45083, University Library of Munich, Germany.
  2. Lilia Quituisaca-Samaniego & Juan Mayorga-Zambrano & Paúl Medina, 2013. "Simulación estocástica de esquemas piramidales tipo Ponzi," Analítika, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, vol. 6(2), pages 51-66, Diciembre.
  3. Juan Mayorga-Zambrano, 2011. "Un modelo matemático para esquemas piramidales tipo Ponzi," Analítika, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, vol. 1(1), pages 123-133, Junio.

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