Reaction-Diffusion-Branching Models of Stock Price Fluctuations

Abstract

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] 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.

4 pages, 3 figures

References in corpus (3)

• Price Variations in a Stock Market With Many Agents
• The Reaction-Diffusion Front for $A+B\to \varnothing$ in One Dimension
• Diffusion-Limited Annihilation with Initially Separated Reactants

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