  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.
