Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
|Number of pages||8|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 1 Mar 1999|
Scopus Subject Areas
- Statistics and Probability
- Condensed Matter Physics