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A simple probabilistic approach of the Yard-Sale model

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  • Chorro, Christophe

Abstract

We propose in the present paper a probabilistic approach of the so-called Hayes (2002) Yard-Sale model using classical diffusion approximations of Markov chains. We partly recover, at the very least for small and high frequency transactions, recent results of Boghosian (2014a) and Boghosian et al. (2015) concerning both wealth condensation in the absence of redistribution mechanisms and steady state distributions when a uniform capital taxation is imposed.

Suggested Citation

  • Chorro, Christophe, 2016. "A simple probabilistic approach of the Yard-Sale model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 35-40.
    • Handle: RePEc:eee:stapro:v:112:y:2016:i:c:p:35-40
    DOI: 10.1016/j.spl.2016.01.012
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    References listed on IDEAS

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    1. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Post-Print halshs-01162452, HAL.
    2. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    3. Fernholz, Ricardo & Fernholz, Robert, 2014. "Instability and concentration in the distribution of wealth," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 251-269.
    4. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Documents de travail du Centre d'Economie de la Sorbonne 15024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01162452, HAL.
    6. Bruce M. Boghosian, 2014. "Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law," Papers 1407.6851, arXiv.org.
    7. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    8. Anirban Chakraborti, 2002. "Distributions Of Money In Model Markets Of Economy," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(10), pages 1315-1321.
    9. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Documents de travail du Centre d'Economie de la Sorbonne 15024r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2015.
    10. S. Ispolatov & P.L. Krapivsky & S. Redner, 1998. "Wealth distributions in asset exchange models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 2(2), pages 267-276, March.
    11. Sitabhra Sinha, 2003. "Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth," Papers cond-mat/0304324, arXiv.org.
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    Cited by:

    1. Lima, Hugo & Vieira, Allan R. & Anteneodo, Celia, 2022. "Nonlinear redistribution of wealth from a stochastic approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. David W. Cohen & Bruce M. Boghosian, 2023. "Bounding the approach to oligarchy in a variant of the yard-sale model," Papers 2310.16098, arXiv.org.
    3. Christoph Borgers & Claude Greengard, 2023. "A new probabilistic analysis of the yard-sale model," Papers 2308.01485, arXiv.org.
    4. Bouleau, Nicolas & Chorro, Christophe, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 379-395.
    5. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01138383, HAL.
    6. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Post-Print hal-01138383, HAL.

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