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Trading leads to scale-free self-organization

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  • M. Ebert
  • W. Paul

Abstract

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribution of trading volumes and price-returns. The origin of the Pareto-like wealth distribution, however, remained obscure. Here we show that it is the process of trading itself that under two mild assumptions spontaneously leads to a self-organization of the market with a Pareto-like wealth distribution for the market participants and at the same time to a scale-free behavior of return fluctuations. These assumptions are (i) everybody trades proportional to his current capacity and (ii) supply and demand determine the relative value of the goods.

Suggested Citation

  • M. Ebert & W. Paul, 2009. "Trading leads to scale-free self-organization," Papers 0905.4815, arXiv.org.
    • Handle: RePEc:arx:papers:0905.4815
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