Reaction–diffusion–branching models of stock price fluctuations

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