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Reaction-Diffusion-Branching Models of Stock Price Fluctuations

Lei-Han Tang·Guang-Shan Tian
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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.

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Lei-Han Tang, Guang-Shan Tian. 1998-11-09. Reaction-Diffusion-Branching Models of Stock Price Fluctuations. https://doi.org/10.1016/s0378-4371(98)00549-4

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