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Wealth distribution in presence of debts. A Fokker--Planck description

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  • Marco Torregrossa
  • Giuseppe Toscani

Abstract

We consider here a Fokker--Planck equation with variable coefficient of diffusion which appears in the modeling of the wealth distribution in a multi-agent society. At difference with previous studies, to describe a society in which agents can have debts, we allow the wealth variable to be negative. It is shown that, even starting with debts, if the initial mean wealth is assumed positive, the solution of the Fokker--Planck equation is such that debts are absorbed in time, and a unique equilibrium density located in the positive part of the real axis will be reached.

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  • Marco Torregrossa & Giuseppe Toscani, 2017. "Wealth distribution in presence of debts. A Fokker--Planck description," Papers 1709.09858, arXiv.org.
    • Handle: RePEc:arx:papers:1709.09858
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    References listed on IDEAS

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    1. Federico Bassetti & Giuseppe Toscani, 2010. "Explicit equilibria in a kinetic model of gambling," Papers 1002.3689, arXiv.org.
    2. Düring, Bertram & Matthes, Daniel & Toscani, Giuseppe, 2008. "A Boltzmann-type approach to the formation of wealth distribution curves," CoFE Discussion Papers 08/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    3. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    4. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
    5. 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.
    6. Düring, Bertram & Matthes, Daniel & Toscani, Giuseppe, 2008. "Kinetic equations modelling wealth redistribution: A comparison of approaches," CoFE Discussion Papers 08/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    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. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
    9. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Master equation for a kinetic model of trading market and its analytic solution," Papers cond-mat/0501413, arXiv.org, revised Aug 2005.
    10. Düring, Bertram & Toscani, Giuseppe, 2008. "International and domestic trading and wealth distribution," CoFE Discussion Papers 08/02, University of Konstanz, Center of Finance and Econometrics (CoFE).
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