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Laplace transform analysis of a multiplicative asset transfer model

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  • Andrey Sokolov
  • Andrew Melatos
  • Tien Kieu

Abstract

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of $f\in(0,1)$. The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

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  • Andrey Sokolov & Andrew Melatos & Tien Kieu, 2010. "Laplace transform analysis of a multiplicative asset transfer model," Papers 1004.5169, arXiv.org.
    • Handle: RePEc:arx:papers:1004.5169
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    1. A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 135-149, November.
    2. M. Rusydi & Sardar M. N. Islam, 2007. "Market Models and Applications," Palgrave Macmillan Books, in: Quantitative Exchange Rate Economics in Developing Countries, chapter 4, pages 45-62, Palgrave Macmillan.
    3. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
    4. 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.
    5. Ali Saif, M. & Gade, Prashant M., 2007. "Emergence of power-law in a market with mixed models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 448-456.
    6. A. Chakraborti & B.K. Chakrabarti, 2000. "Statistical mechanics of money: how saving propensity affects its distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 17(1), pages 167-170, September.
    7. M. Patriarca & A. Chakraborti & E. Heinsalu & G. Germano, 2007. "Relaxation in statistical many-agent economy models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 219-224, May.
    8. Anirban Chakraborti & Bikas K. Chakrabarti, 2000. "Statistical mechanics of money: How saving propensity affects its distribution," Papers cond-mat/0004256, arXiv.org, revised Jun 2000.
    9. Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 388-414.
    10. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
    11. Anirban Chakraborti & Marco Patriarca, 2008. "Gamma-distribution and wealth inequality," Papers 0802.4410, arXiv.org.
    12. 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.
    13. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
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    Cited by:

    1. Diniz, M. & Mendes, F.M., 2012. "Effects of taxation on money distribution," International Review of Financial Analysis, Elsevier, vol. 23(C), pages 81-85.

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