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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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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 2 (September)
Pages: 190-201

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:190-201

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Ponzi scheme Charles Ponzi Differential equation Investment Rate of return;

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References

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  1. Stephen A. O'Connell & Stephen P. Zeldes, . "Rational Ponzi Games," Rodney L. White Center for Financial Research Working Papers 18-86, Wharton School Rodney L. White Center for Financial Research.
    • 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 431-50, August.
  2. 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.
  3. Olivier Jean Blanchard & Philippe Weil, 1992. "Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games Under Uncertainty," NBER Working Papers 3992, National Bureau of Economic Research, Inc.
  4. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.
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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, 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, vol. 1(1), pages 123-133, Junio.

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