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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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  • Artzrouni, Marc, 2009. "The mathematics of Ponzi schemes," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 190-201, September.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:190-201
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    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.
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    5. 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.
    6. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.
    7. 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. Hofstetter, Marc & Mejía, Daniel & Rosas, José Nicolás & Urrutia, Miguel, 2018. "Ponzi schemes and the financial sector: DMG and DRFE in Colombia," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 18-33.
    2. DUGULEANĂ Andreea Raluca & TĂNĂSESCU Cristina Roxana & DUGULEANĂ Mihai, 2024. "A New Approach To Create Sustained Ponzi-Like Systems By Incorporating Perpetual Liquidity And Time Epochs," Management of Sustainable Development, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 16(1), pages 37-44, June.
    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. 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.
    5. Phuong Duy Huynh & Son Hoang Dau & Xiaodong Li & Phuc Luong & Emanuele Viterbo, 2023. "Improving the Accuracy of Transaction-Based Ponzi Detection on Ethereum," Papers 2308.16391, arXiv.org, revised Jul 2024.
    6. Misha Perepelitsa, 2021. "Investing in crypto: speculative bubbles and cyclic stochastic price pumps," Papers 2111.11315, arXiv.org, revised Oct 2022.
    7. Ajithakumari Vijayappan Nair Biju & Ann Susan Thomas, 2023. "Uncertainties and ambivalence in the crypto market: an urgent need for a regional crypto regulation," SN Business & Economics, Springer, vol. 3(8), pages 1-21, August.
    8. Yong Shi & Bo Li & Wen Long, 2019. "A Pyramid Scheme Model Based on "Consumption Rebate" Frauds," Papers 1904.08136, arXiv.org, revised Jun 2019.
    9. 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.
    10. Chengxiang Jin & Jiajun Zhou & Jie Jin & Jiajing Wu & Qi Xuan, 2022. "Time-aware Metapath Feature Augmentation for Ponzi Detection in Ethereum," Papers 2210.16863, arXiv.org, revised Apr 2024.
    11. Parodi, Bernhard R., 2014. "A Ponzi scheme exposed to volatile markets," MPRA Paper 60584, University Library of Munich, Germany.
    12. 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.
    13. Parodi, Bernhard R., 2013. "Abc-Modell eines Ponzi-Systems [Abc-model of a Ponzi system]," MPRA Paper 45083, University Library of Munich, Germany.
    14. Sara Cerasoli & Amilcare Porporato, 2023. "Optimal Resource Allocation for Carbon Mitigation," Sustainability, MDPI, vol. 15(13), pages 1-22, June.

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    More about this item

    Keywords

    Ponzi scheme Charles Ponzi Differential equation Investment Rate of return;

    JEL classification:

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

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