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The mathematics of Ponzi schemes


  • Artzrouni, Marc


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.

Suggested Citation

  • Artzrouni, Marc, 2009. "The mathematics of Ponzi schemes," MPRA Paper 14420, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:14420

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    References listed on IDEAS

    1. Blanchard Olivier & Weil Philippe, 2001. "Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(2), pages 1-23, November.
    2. O'Connell, Stephen A & Zeldes, Stephen P, 1988. "Rational Ponzi Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 431-450, August.
    3. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.
    4. Forslid, Rikard, 1998. "External Debt and Ponzi-Games in a Small Open Economy with Endogenous Growth," Journal of Macroeconomics, Elsevier, vol. 20(2), pages 341-349, April.
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    Cited by:

    1. Parodi, Bernhard R., 2014. "A Ponzi scheme exposed to volatile markets," MPRA Paper 60584, University Library of Munich, Germany.
    2. Zhu, Anding & Fu, Peihua & Zhang, Qinghe & Chen, Zhenyue, 2017. "Ponzi scheme diffusion in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 128-136.
    3. Juan Mayorga-Zambrano, 2011. "Un modelo matemático para esquemas piramidales tipo Ponzi," Analítika, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, vol. 1(1), pages 123-133, Junio.
    4. Parodi, Bernhard R., 2013. "Abc-Modell eines Ponzi-Systems
      [Abc-model of a Ponzi system]
      ," MPRA Paper 45083, University Library of Munich, Germany.
    5. 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, vol. 6(2), pages 51-66, Diciembre.
    6. Mário Cunha & Hélder Valente & Paulo B. Vasconcelos, 2013. "Ponzi schemes: computer simulation," OBEGEF Working Papers 023, OBEGEF - Observatório de Economia e Gestão de Fraude;OBEGEF Working Papers on Fraud and Corruption.
    7. Marc Hofstetter & Daniel Mejía & José Nicolás Rosas & Miguel Urrutia, 2017. "Ponzi Schemes and the Financial Sector: DMG and DRFE in Colombia," DOCUMENTOS CEDE 015609, UNIVERSIDAD DE LOS ANDES-CEDE.

    More about this item


    Ponzi scheme; differential equation; market; bond;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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