Power laws of wealth, market order volumes and market returns

Sorin Solomon*, Peter Richmond

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

100 Scopus citations

Abstract

Using the Generalized Lotka Volterra model adapted to deal with mutiagent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue that 'fair play' for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α ∼ 3/2. In particular, we relate it to the average number of individuals L depending on the average wealth: α ∼ L/(L-1). Then we connect it to certain power exponents characterizing the stock markets. We find that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β ∼ α ∼ 3/2. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ ∼ 2α ∼ 3. These results are consistent with recent experimental measurements of these power law exponents (S. Maslov, M. Mills, Physica A 299 (2001) 234 for β P. Gopikrishnan et al., Phys. Rev. E 60 (1999) 5305 for γ).

Original languageEnglish
Pages (from-to)188-197
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Volume299
Issue number1-2
DOIs
StatePublished - 1 Oct 2001
EventApplication of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic
Duration: 8 Feb 200110 Feb 2001

Keywords

  • Lotka-Volterra
  • Market returns
  • Pareto-Zipf
  • Power law
  • Random multiplicative process
  • Wealth distribution

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